# MATH 130 - Spring 2018 Calculus I

Professor: Erika L.C. King
Email:eking@hws.edu
Office: Lansing 304
Phone: (315) 781-3355

Office Hours: M 1:30-3:00pm, W 1:30-3:00pm, Th 9:30-10:30am, F 9:30-10:30am and by appointment

Section 2 Class: MWF 11:15am-12:10pm in Eaton 110
Section 2 Lab: Th 11:55am-1:20pm in Gulick 2000

Section 3 Class: MWF 12:20-1:15pm in Eaton 110
Section 3 Lab: Th 1:30-2:55pm in Gulick 2000

Course Syllabus for Section 2
Course Syllabus for Section 3
***Note that these syllabi are essentially the same -- the main difference is the Final Exam schedule.***

Course Homework Guidelines

Math Intern, Phoebe Cai's Office Hours in Lansing 310: Su 4:00-6:00pm and 7:00-10:00pm, M-Th 3:00-6:00pm and 7:00-10:00pm

### READING/EXAM WEEK: May 2 - May 8

Check out the Lab Key for the Week 14 Lab!

Lost your final review sheet? Here is a copy. NOTE: This is for Section 3! Section 2 has a DIFFERENT exam time!!!

Review Session: Friday, May 4th from 10:30am until Noon in Eaton 110. Attendance optional. Come prepared with questions!

Office Hours:

• Wednesday, May 2nd: 2:00pm-4:00pm
• Thursday, May 3rd: 1:00pm-3:00pm
• Monday, May 7th: 11:30am-1:30pm
• By appointment

Final Exam:

• For Section 2: the final exam is on Tuesday, May 8th from 1:30pm until 4:30pm in Eaton 110.
• For Section 3: the final exam is on Sunday, May 6th from 1:30pm until 4:30pm in Eaton 110.

Have a great summer! Keep in touch!

### WEEK 15: April 30 - May 1

Homework due Monday, April 30:

• Review the group work and notes from Friday's class. Recall that we worked on Section 4.9: 25, 27, 31, 35, 42, 61, 65, 85, 89, 101, 107, 108, and 109. Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• If there is a problem from Friday's board-work you would like to discuss, put it on the board when you arrive to class! If your group didn't get to finish your problem, put it on the board when you get to class.
• No Lab due this Monday! In fact, there are NO MORE Labs!
• Work practice exercises on Section 4.9 on WeBWorK. Read the directions and hints carefully BEFORE submitting! The sixth and eighth question only allow ONE submission!!! Be sure you know why your answers are good even if you don't need to explain that on WeBWorK! Remember that you can preview your work before you submit it! This will help to avoid using incorrect notation or autofill. This is due Monday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• If there is time and interest, at the beginning of class we will discuss one WeBWorK problem. Email me by 10:305am on Monday if there is a problem you would like to discuss. The most requested problem will be selected.
• There is no Reading Assignment due on Monday! In fact, there are NO MORE Reading Assignments!

### WEEK 14: April 23 - April 27

Homework due Monday, April 23:

• Review the group work and notes from Friday's class. Recall that we worked on Section 4.7: 15, 17, 21, 25, 27, 30, 40, 41, 46, 53 and 54; and the question: Evaluate $\lim_{x\to 0^+}x\ln(\tan x)$. Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• No Lab due this Monday!
• Work practice exercises on Section 4.7 on WeBWorK. Read the directions and hints carefully BEFORE submitting! The first and last question only allow ONE submission!!! Be sure you know why your answers are good even if you don't need to explain that on WeBWorK! Remember that you can preview your work before you submit it! This will help to avoid using incorrect notation or autofill. This is due Monday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.

Homework due Wednesday, April 25:

• Review the groupwork exercises and notes from Monday's class. Recall that we worked on Section 4.7: 55, 57, 59, 60, 61, 62, 65 and 66. Make sure you feel confident with these questions, especially showing all the steps to obtain the answer. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• Finish working on the example we started in class on Monday about the rectangular pen. Make sure the steps we completed in class make sense, then: Section 2: You are on Step 5: Find critical numbers and appropriate extremum. Section 3: You need to do Step 4 (Find the domain of the objective function) before you move to Step 5. Both Sections should finish the example and be ready to discuss it at the beginning of Wednesday's class.
• Work this exercise on Section 4.4 on WeBWorK. Read the directions and hints carefully BEFORE submitting! Remember that you can preview your work before you submit it! This will help to avoid using incorrect notation or autofill. This is due Wednesday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Work a few more exercises on Section 4.4 on WeBWorK. Read the directions and hints carefully BEFORE submitting! Remember that you can preview your work before you submit it! This will help to avoid using incorrect notation or autofill. This is due Wednesday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• There is no Reading Assignment due on Wednesday! In fact, there are NO MORE Reading Assignments!
• ***Remember to bring a laptop or phone with you to lab on Thursday on which you can do your evaluations!***
• ***Think about what you might like/be able to bring to the lab party. Pair or triple up with your friends to bring something! There will be a sign up sheet on Wednesday.***
• Get started on the assignment posted below, due Friday, NOW! (Hopefully you are reading this on Monday!)

***Remember to bring a laptop or phone with you to lab on Thursday on which you can do your evaluations!*** I will also have a few tablets in case you forget!

Homework due Friday, April 27:

• Review the notes and exercises from Wednesday's class. Recall that the exercises we worked on in group work at the end of class were Section 4.4: 17 and 21, and the exercise on the handout (be sure to pick up a handout in lab if you didn't get one in Wednesday!). Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• Work a few exercises on Section 4.4 on WeBWorK. Read the directions and and hints carefully! This is due Friday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Try a few more exercises from Section 4.4 such as Exercise 13 and Exercise 31. The more you try the more comfortable you will feel with them!
• Complete the Main Exercises Assignment for Week 14 on this handout. This is due Friday at the beginning of class.
• There is no Reading Assignment due on Friday! In fact, there are NO MORE Reading Assignments!

### WEEK 13: April 16 - April 20

Remember that our third exam is Thursday, April 19th in lab. The exam will cover sections 3.9-4.3, and 4.6.

Homework due Monday, April 16:

• Review the group work and notes from Friday's class. Recall that we worked on Section 4.6: 7, 9, 11 and 13; Section 4.3: 17, 21, 25 and 58; WeBWorK questions 1 and 8 from the assignment due Friday; and the question: Show $f(x)=-2x^{15}-5x+21$ has exactly one real root. Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• Work through the proof of the Mean Value Theorem. Isn't it amazing! Write down any questions you have and bring them to class on Monday.
• If you haven't already, start reviewing for Exam 3. (Actually, we review all the time! But I mean in a methodical way...) Make yourself a review sheet! I will provide one for you as well, but you will get more out of making one than reading one! Make one now and then compare it to the one I give you early in the week.
• Week 12 Lab is due at the beginning of Monday's class! One from each group. Be sure you meet with your group to review each other's final write-ups prior to Monday's class, so that everyone agrees that each group member's set of solutions is a good one. I will roll the die to see which group member will turn in her/hir/his paper. Be sure you send your lab to class with someone else if there is a reason you cannot be there!!!
• Work practice exercises on Section 4.6 on WeBWorK. Read the directions and hints carefully BEFORE submitting! The first and last question only allow ONE submission!!! Be sure you know why your answers are good even if you don't need to explain that on WeBWorK! Remember that you can preview your work before you submit it! This will help to avoid using incorrect notation or autofill. This is due Monday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Guess what? NO Reading Assignment due Monday! Reread sections 4.3 and 4.6 and solidify this material, letting me know if there are specific questions you would like to discuss! Also review the reading from Section 4.7 -- there is a lot of material in that section!

Since we have an exam this week, there will be NO Main Exercises assignment due on Friday!

Here is the Lab Key for the Week 10 Lab. Be sure to read it to make sure the material makes sense and let me know if you have any questions. Also note the level of detail that is necessary for complete solutions.

ERROR! Note there is an error in the Extra Fun Week 10 Lab Key above. The first question should have $\frac{3}{10}$ m/min as the solution!

Here is the Lab Key for the Week 11 Lab. Be sure to read it to make sure the material makes sense and let me know if you have any questions. Also note the level of detail that is necessary for complete solutions.

Homework due Wednesday, April 18:

• Review the groupwork exercises and notes from Monday's class. Recall that we worked on Section 4.6: 17, 19, 21, 23, 25, 26, 27, 29, 33 and the proof of Theorem 4.12. Make sure you feel confident with these questions, especially showing all the steps to obtain the answer. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• Work a few practice exercises on Section 4.7 on WeBWorK. This will help you review some derivatives too! Read the directions and hints carefully BEFORE submitting! Remember that you can preview your work before you submit it! This will help to avoid using incorrect notation or autofill. This is due Wednesday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Read Section 4.4 (pages 270-274). Then complete the Reading Assignment for that section on this handout. Copies of this can be found in the box outside my office. In this section we apply all our maximizing and minimizing skills to real world problems! Go back and review how we found absolute extrema in Sections 4.1 and 4.2. Remember those maximizing profit and minimizing material (for canning fruit) questions we asked at the beginning of the semester? Let's answer them now! Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Wednesday at the beginning of class. It will be considered late if it is turned in after the beginning of class.
• Review for the exam. Check out the Review sheet here. Be sure to bring questions to class!
• Email me if there are particular types of questions you would like to see discussed in class.

Homework due Thursday, April 19:

• Prepare for Exam 3! Have confidence in your abilities!!!
• Here is the Lab Key for the Week 12 Lab. Be sure to read it to make sure the material makes sense and let me know if you have any questions. Also note the level of detail that is necessary for complete solutions.
• Arrive on time to lab in Gulick 2000. Remember that seating is assigned randomly, so wait until you are told where to sit.

Homework due Friday, April 20:

• Review the notes from Wednesday's class. Reread Section 4.7 and make sure the indeterminate forms make sense!
• Work a few practice exercises on Section 4.7 on WeBWorK. Read the directions and hints carefully! This is due Friday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Work a just few more practice exercises on Section 4.7 on WeBWorK. Read the directions and hints carefully! This is due Friday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Recall: THERE IS NO MAIN EXERCISES ASSIGNMENT DUE THIS WEEK!!! :)
• Guess what? NO Reading Assignment due Friday! Reread section 4.7 and solidify this material, letting me know if there are specific questions you would like to discuss! Also review the reading from Section 4.4 to get ready for Optimization!

### WEEK 12: April 9 - April 13

Homework due Monday, April 9:

• Review the group work and notes from Friday's class. Recall that we worked on Section 4.2: 46, 49, 51, 66, 67 and 75, in addition to the questions we were working on Wednesday. Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• Week 11 Lab is due at the beginning of Monday's class! One from each group. Be sure you meet with your group to review each other's final write-ups prior to Monday's class, so that everyone agrees that each group member's set of solutions is a good one. I will roll the die to see which group member will turn in her/hir/his paper. Be sure you send your lab to class with someone else if there is a reason you cannot be there!!!
• Work practice exercises on Section 4.2 on WeBWorK. Read the directions and hints carefully BEFORE submitting! Remember that you can preview your work before you submit it! This will help to avoid using incorrect notation or autofill. This is due Monday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Work practice exercises on Section 4.3 on WeBWorK. Read the directions and hints carefully BEFORE submitting! Remember that you can preview your work before you submit it! This will help to avoid using incorrect notation or autofill. This is due Monday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Guess what? NO Reading Assignment due Monday! Reread sections 4.2 and 4.3 and solidify this material, letting me know if there are specific questions you would like to discuss! If you feel like looking ahead, check out Section 4.7. The reading assignment for Section 4.7 will be due on Wednesday.

Homework due Wednesday, April 11:

• Review the groupwork exercises and notes from Monday's class. Recall that we worked on Section 4.3: 8, 16, 31, 43 and 49. Make sure you feel confident with these questions, especially showing all the steps to obtain the answer. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• Work just a few practice exercises on Section 4.3 on WeBWorK. Read the directions and hints carefully BEFORE submitting! Remember that you can preview your work before you submit it! This will help to avoid using incorrect notation or autofill. This is due Wednesday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Work just a couple more practice exercises on Section 4.3 on WeBWorK. Read the directions and hints carefully BEFORE submitting! Remember that you can preview your work before you submit it! This will help to avoid using incorrect notation or autofill. This is due Wednesday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Read Section 4.7 (pages 297-307). Then complete the Reading Assignment for that section on this handout. Copies of this can be found in the box outside my office. In this section we return to investigate limits a bit more using our new found knowledge of derivatives. Back in chapter 2, we dealt with limits that were of the form $\frac{0}{0}$. When we came across these, we said we had to "do more work" and used tricks like factoring and canceling, multiplying out and canceling, and rationalizing. Those tricks don't always help us, however. Luckily, some mathematicians back in the 1600s and 1700s came up with another alternative which is known as l'H\^opital's Rule. Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Wednesday at the beginning of class. It will be considered late if it is turned in after the beginning of class.

Homework due Friday, April 13 (Happy Friday the 13th!):

• Review the notes from Wednesday's class. Be sure that you took good notes of our proof by contradiction and ask a friend if you didn't!
• At the beginning of Friday's class we will do group work on Rolle's Theorem and Section 4.3. I put these problems on the board at the end of Wednesday's class. If you have a chance, take a look at them ahead of time. They are: Section 4.6: 7, 9, 11 and 13; Section 4.3: 21, 25 and 58; and the question: Show $f(x)=-2x^{15}-5x+21$ has exactly one real root.
• Work on reviewing for our exam next week with the first six of these problems, then do two problems on Rolle's Theorem in this WeBWorK. Read the directions and hints carefully! This is due Friday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Complete the Main Exercises Assignment for Week 12 on this handout. This is due Friday at the beginning of class. I had copies outside my office, but they were all taken. If you need one please let me know and I will put more out! Note that typically you are not required to turn in your main exercises on the handout but this week you are!
• Guess what? NO Reading Assignment due Friday! Reread sections 4.3 and 4.6 and solidify this material, letting me know if there are specific questions you would like to discuss! Also review the reading from Section 4.7 -- there is a lot of material in that section!

### WEEK 11: April 2 - April 6

Homework due Monday, April 2:

• Review the group work and notes from Friday's class. Recall that we worked on Section 3.11: 6, 9, 12, 17, and the first problem form Week 10 Lab Extra Fun. Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• Week 10 Lab is due at the beginning of Monday's class! One from each group. Be sure you meet with your group to review each other's final write-ups prior to Monday's class, so that everyone agrees that each group member's set of solutions is a good one. I will roll the die to see which group member will turn in her/hir/his paper. Be sure you send your lab to class with someone else if there is a reason you cannot be there!!!
• Work practice exercises on Section 4.1 on WeBWorK. Read the directions and hints carefully BEFORE submitting! Remember that you can preview your work before you submit it! This will help to avoid using incorrect notation or autofill. This is due Monday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Guess what? NO Reading Assignment due Monday! Reread sections 3.9 and 3.10 and solidify this material, letting me know if there are specific questions you would like to discuss! If you feel like looking ahead, check out Section 4.3. The reading assignment for Section 4.3 will be due on Wednesday.
• Rework any problems on the exam for which you missed points! Make sure you understand where your errors are and ask if you do not!
• Make plans to come to office hours to discuss your exam and/or questions you have about current material. It would be great if I saw each of you at least once this week! Note that some would like to speak privately about the exam so there may be parts of office hours where we will not be working in a group in office hours but rather one-on-one. If the door is open during office hours, come on in! If it is closed or mostly closed, wait until the student and I are finished discussing their work privately. Thank you!

Homework due Wednesday, April 4:

• Review the groupwork exercises and notes from Monday's class. Recall that we worked on Section 4.1: 11, 13, 15, 17, 19, 21, 31a, 33a, 39ab, 46ab, and 61ab. Make sure you feel confident with these questions, especially showing all the steps to obtain the answer. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• Work practice exercises on Section 4.1 on WeBWorK. Read the definitions carefully! Remember that you can preview your work before you submit it! This will help to avoid using incorrect notation or autofill. This is due Wednesday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Read Section 4.3 (pages 260-267). Then complete the Reading Assignment for that section on this handout. Copies of this can be found in the box outside my office. Now we have the opportunity to bring lots of the information we have learned this semester (and in previous mathematics classes!) together to figure out how to graph functions with just pencil and paper! Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Wednesday at the beginning of class. It will be considered late if it is turned in after the beginning of class.
• Rework any problems on the exam for which you missed points! Make sure you understand where your errors are and ask if you do not!
• Make plans to come to office hours to discuss your exam and/or questions you have about current material. It would be great if I saw each of you at least once this week! Note that some would like to speak privately about the exam so there may be parts of office hours where we will not be working in a group in office hours but rather one-on-one. If the door is open during office hours, come on in! If it is closed or mostly closed, wait until the student and I are finished discussing their work privately. Thank you!

Homework due Friday, April 6:

• Review the notes and exercises from Wednesday's class. Recall that the exercises we worked on in group work at the end of class were Section 4.2: 12, 14, 25, 27, 37, 41, 43, 45 and 47. Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• At the beginning of Friday's class we will do group work on some of the problems from Wednesday together with some new problems. If there are particular problems you want to be sure are seen again from Wednesday's work, let me know by Friday at 10:30am.
• Work the first practice exercise on Section 4.2 on WeBWorK. Read the directions and hints carefully! This is due Friday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Work the more practice exercises on Section 4.2 on WeBWorK. Read the directions and hints carefully! This is due Friday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Complete the Main Exercises Assignment for Week 11 on this handout. This is due Friday at the beginning of class.
• Read Section 4.6 (pages 290-294). Then complete the Reading Assignment for that section on this handout. Copies of this can be found in the box outside my office. The Mean Value Theorem is an incredibly important theorem in calculus used to prove many other theorems, not the least of which is the Fundamental Theorem of Calculus, which is studied in Calculus II (MATH 131). Rolle's Theorem can be thought of as a special case of the Mean Value Theorem, but we look at it first in part because it is visually easier to grasp and in part because we can use it to prove the Mean Value Theorem! :-) Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Friday at the beginning of class. It will be considered late if it is turned in after the beginning of class.

### WEEK 10: March 26 - March 30

Have a great spring break!!!

Homework due Monday, March 26:

• If you were not in class on Friday, March 16, you are responsible for getting the notes from someone!!! Be sure to do this ASAP. After you have the notes, you are encouraged to ask me any questions in office hours about them or the material in general.
• Review the group work and notes from Friday the 16th's class. Recall that we worked on Section 3.9: 37, 40, 49, 51, 55, 57, 65, 69, 71, 81, 89, 97 and 101. Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• No Lab due this Monday!
• Work practice exercises on Section 3.10 on WeBWorK. Read the directions and hints carefully BEFORE submitting! Remember that you can preview your work before you submit it! This will help to avoid using incorrect notation or autofill. This is due Monday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Guess what? NO Reading Assignment due Monday! Reread sections 3.9 and 3.10 and solidify this material, letting me know if there are specific questions you would like to discuss! If you feel like looking ahead, check out Section 4.1. The reading assignment for Section 4.1 will be due on Wednesday.

Homework due Wednesday, March 28:

• Review the groupwork exercises and notes from Monday's class. Recall that we worked on Section 3.10: 11, 14, 25, 27, 31, 33, 39, 47, 49, 51 and 53. Make sure you feel confident with these questions, especially showing all the steps to obtain the answer. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• Work practice exercises on derivatives of inverse functions and related rates from Sections 3.10 and 3.11 on WeBWorK. Read the definitions carefully! Remember that you can preview your work before you submit it! This will help to avoid using incorrect notation or autofill. This is due Wednesday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Read Section 4.1 (pages 236-242). Then complete the Reading Assignment for that section on this handout. Copies of this can be found in the box outside my office. In chapter 4 we will look more deeply into what information the derivative can tell us about the original function. This first section focuses on how the derivative can help us find places where our function has extreme values -- locally and globally. Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Wednesday at the beginning of class. It will be considered late if it is turned in after the beginning of class.

Homework due Friday, March 30:

• Review the exercises and other notes from Wednesday's class. Recall that the exercises we worked on in group work included: proving Theorem 3.23 using properties of inverse functions and implicit differentiation, WeBWorK problems 2 and 3 that were due on Wednesday, Examples 3 and 4 on the handout, and the extra problem was to do Example 2 on the handout. Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• Work practice exercises on Section 3.11 on WeBWorK. Read the directions and hints carefully! This is due Friday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Complete the Main Exercises Assignment for Week 10 on this handout. This is due Friday at the beginning of class.
• Read Section 4.2 (pages 245-256). Then complete the Reading Assignment for that section on this handout. Copies of this can be found in the box outside my office. In the previous section we learned about what local extrema are, but how do we find them? In this section we figure out how to determine whether or not our critical numbers are local minimums and maximums. We also find out about how derivatives can tell us many other features of a function, so many other features that afterwards we will be able to graph functions by hand (no calculators needed!)! Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Friday at the beginning of class. It will be considered late if it is turned in after the beginning of class.

### WEEK 9: March 12 - March 16

Remember that our second exam is Thursday, March 15th in lab. The exam will cover sections 2.5, 2.6, 3.1-3.5, 3.7 and 3.8.

BONUS! Want some extra practice with compositions of functions? Try these problems on WeBWorK. Read the directions carefully! This is due SUNDAY, March 11 at 5:00pm online.

BONUS! Work these BONUS exercises for more practice on chain rule and combining chain rule with product rule with problems from Section 3.7 on WeBWorK. Read the directions and hints carefully! This is due SUNDAY, March 11 at 6:00pm online.

Here is the Lab Key for the Week 7 Lab. Be sure to read it to make sure the material makes sense and let me know if you have any questions. Also note the level of detail that is necessary for complete solutions.

Homework due Monday, March 12:

• Review the group work and notes from Friday's class. Recall that we worked on Section 3.7: 17, 23, 37, 49, 51, 53, 55, 59, 61, 69, 71, 83, 89 and 97. Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• Section 3: Finish finding $\frac{dy}{dx}$ for the last question we were working on in class on Friday. Then try to find the second derivative! Be ready to share your work at the beginning of class on Monday.
• Week 8 Lab is due at the beginning of Monday's class! One from each group. Be sure you meet with your group to review each other's final write-ups prior to Monday's class, so that everyone agrees that each group member's set of solutions is a good one. I will roll the die to see which group member will turn in her/hir/his paper. Be sure you send your lab to class with someone else if there is a reason you cannot be there!!!
• If you haven't already, start reviewing for Exam 2. Make yourself a review sheet! I will provide one for you as well (posted on Monday or Tuesday), but you will get more out of making one than reading one! Make one now and then compare it to the one I give you early in the week.
• Work practice exercises on Section 3.8 on WeBWorK. Read the directions and hints carefully BEFORE submitting! Remember that you can preview your work before you submit it! This will help to avoid using incorrect notation or autofill. This is due Monday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Read Section 3.9 (pages 203-210). Then complete the Reading Assignment for that section on this handout. Copies of this can be found in the box outside my office. This reading discusses the derivative of $y=\ln x$ as well as the general forms of derivatives of exponential and logarithmic functions. Most exciting, the reading describes logarithmic differentiation, which allows us to take derivatives of more complicated functions! A key to many of the ideas in this section is the fact that $y=e^x$ and $y=\ln x$ are inverse functions, which we discussed at the beginning of the semester. Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Monday at the beginning of class. It will be considered late if it is turned in after the beginning of class.

Since we have an exam this week, there will be NO Main Exercises assignment due on Friday!

Homework due Wednesday, March 14, PI DAY!!!:

• Review the groupwork exercises and notes from Monday's class. Recall that we worked on Section 3.8: 9, 12, 13, 14, 17, 22, 23, 25, 27, 29, 31, 33, 35, 49, 51, 57, 83 and 85, and also Section 3.7: 60, 62 and 70. Make sure you feel confident with these questions, especially showing all the steps to obtain the answer. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• Section 3: Make sure you take a look at the exercises I put on the board at the end of class (the second half of those above). Let me know if there are any you would like to discuss in the second half of class on Wednesday. Especially spend time with exercises 31, 33, 35 and 85 where you are looking at second derivatives using implicit differentiation.
• Work practice exercises on implicit differentiation and some review in this WeBWorK. Read the definitions carefully! Remember that you can preview your work before you submit it! This will help to avoid using incorrect notation or autofill. This is due Wednesday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Read Section 3.10 (pages 214-221). Then complete the Reading Assignment for that section on this handout. Copies of this can be found in the box outside my office. This reading discusses the derivatives of inverse trigonometric functions. Notice that the derivatives of inverse trigonometric functions are algebraic not trigonometric! Many of the ideas we discussed at the beginning of the semester will be important here! Remember that we can use the notation of $\arcsin x$ for $\sin^{-1}x$, etc. Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Wednesday at the beginning of class. It will be considered late if it is turned in after the beginning of class.
• Review for the exam. Check out the Review sheet here. Be sure to bring questions to class!
• Email me if there are particular types of questions you would like to see discussed in class.

Homework due Thursday, March 15:

• Prepare for Exam 2! Have confidence in your abilities!!!
• Here is the Lab Key for the Week 8 Lab. Be sure to read it to make sure the material makes sense and let me know if you have any questions. Also note the level of detail that is necessary for complete solutions.
• Arrive on time to lab in Gulick 2000. Remember that seating is assigned randomly, so wait until you are told where to sit.

Homework due Friday, March 16:

• Review the notes from Wednesday's class. Bring any questions you have to Friday's class.
• Work practice exercises on Sections 3.9 on WeBWorK. Read the directions and hints carefully! This is due Friday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Recall: THERE IS NO MAIN EXERCISES ASSIGNMENT DUE THIS WEEK!!! :)
• Read Section 3.11 (pages 224-227). Then complete the Reading Assignment for that section on this handout. Copies of this can be found in the box outside my office (Wednesday afternoon!). This reading looks at applying what we have been learning about instantaneous rates of change, implicit differentiation and more to real life circumstances! Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Friday at the beginning of class. It will be considered late if it is turned in after the beginning of class.

### WEEK 8: March 5 - March 9

BONUS! Work these BONUS exercises on Section 3.3 on WeBWorK. Read the definitions carefully! This is due SUNDAY, March 4 at 5:00pm online.

Here is the Lab Key for the Week 6 Lab. Be sure to read it to make sure the material makes sense and let me know if you have any questions. Also note the level of detail that is necessary for complete solutions.

Homework due Monday, March 5:

• Review the group work and notes from Friday's class. Recall that we worked on Section 3.4: 13, 27, 31, 53, 55, 57, 61, 63, 69 and 77. Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• Section 2: We did not get to do the last example. Be sure to check out the other trick with limits in Example 1b on pages 164-165! (Dividing the numerator and denominator by $x$!)
• Week 7 Lab is due at the beginning of Monday's class! One from each group. Be sure you meet with your group to review each other's final write-ups prior to Monday's class, so that everyone agrees that each group member's set of solutions is a good one. I will roll the die to see which group member will turn in her/hir/his paper. Be sure you send your lab to class with someone else if there is a reason you cannot be there!!!
• Work practice exercises on special limits in Section 3.5 on WeBWorK. Read the directions and hints carefully BEFORE submitting! Remember that you can preview your work before you submit it! This will help to avoid using incorrect notation or autofill. This is due Monday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Read Section 3.7 (pages 185-191). Then complete the Reading Assignment for that section on this handout. Copies of this can be found in the box outside my office. We have learned how to take the derivative of real number powers of $x$, of $e^x$, and of products and quotients involving these functions. Now we expand our knowledge even further to compositions of functions! Check out the proof of the Chain Rule at the end of the section! Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Monday at the beginning of class. It will be considered late if it is turned in after the beginning of class.

Homework due Wednesday, March 7:

• If you haven't come to office hours to touch base since I returned the exams, please do so this week, especially if you earned less than 80 points on the exam!
• Review the groupwork exercises and notes from Monday's class. Recall that we worked on Section 3.5: 8-16 and 51. Make sure you feel confident with these questions, especially showing all the steps to obtain the answer. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• Work practice exercises on derivatives of trigonometric functions in Section 3.5 on WeBWorK. Read the definitions carefully! Remember that you can preview your work before you submit it! This will help to avoid using incorrect notation or autofill. This is due Wednesday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Read Section 3.8 (pages 195-199). Then complete the Reading Assignment for that section on this handout. Copies of this can be found in the box outside my office. This section uses what we learned about the Chain Rule in the last section to do some really amazing things! This reading helps us figure out how to find the rate of change of one variable in terms of another without having a function that explicitly relates the two variables! Our understanding of the notation of derivatives is vitally important here. Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Wednesday at the beginning of class. It will be considered late if it is turned in after the beginning of class.
• As we start to learn more derivative formulas and special limits, I highly recommend that you make flashcards to help remember them!

Homework due Friday, March 9:

• Remember: If you earned less than 80 out of 114 on the first exam, be sure to come to office hours this week! YOU ARE REQUIRED!!! Everyone is encouraged to stop by to discuss the exam and any questions you have, but those who earned less than 80 are required to do so! Rework the problems from the first exam. If you would like a blank copy, come to my office and I will provide you with one. Make sure these questions make sense and that you understand the concepts!
• Review the exercises and other notes from Wednesday's class. Recall that the exercises we worked on in group work included: 21, 23, 31, 38, 43, 46, 49, 59, 65a, 67, 68 and 81 from Section 3.5. Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• Work warm-up practice exercises on the chain rule from Section 3.7 on WeBWorK. Read the directions and hints carefully! This is due Friday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Now work on a few more challenging exercises on the chain rule from Section 3.7 on WeBWorK. Read the directions and hints carefully! This is due Friday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Complete the Main Exercises Assignment for Week 8 on this handout. This is due Friday at the beginning of class.
• Guess what? NO Reading Assignment due Friday! Reread sections 3.5 and 3.7 and solidify this material, letting me know if there are specific questions you would like to discuss! If you feel like looking ahead, check out Section 3.9. The reading assignment for Section 3.9 will be due on Monday.

### WEEK 7: February 26 - March 2

Homework due Monday, February 26:

• Review the group work and notes from Friday's class. Recall that we worked on Section 3.1: 14, 23, 33, 37, 40, 41, 46, 51, 53, 58 and 61. Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• Week 6 Lab is due at the beginning of Monday's class! One from each group. Be sure you meet with your group to review each other's final write-ups prior to Monday's class, so that everyone agrees that each group member's set of solutions is a good one. I will roll the die to see which group member will turn in her/hir/his paper. Be sure you send your lab to class with someone else if there is a reason you cannot be there!!!
• Work practice exercises on Section 3.2 on WeBWorK. Read the directions and hints carefully BEFORE submitting! Remember that you can preview your work before you submit it! This will help to avoid using incorrect notation or autofill. This is due Monday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Read Section 3.4 (pages 153-159). Then complete the Reading Assignment for that section on this handout. Copies of this can be found in the box outside my office. In the last section we learned some basic differentiation rules that we can use to avoid using the definition of the derivative to differentiate in some cases. There we looked at sums and differences, but we did not look at products or quotients. As you will see, it is not as straightforward to deal with products as it is to deal with sums. However, there is a way! Read on! Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Monday at the beginning of class. It will be considered late if it is turned in after the beginning of class.

Homework due Wednesday, February 28:

• Review the groupwork exercises and notes from Monday's class. Recall that we worked on Section 3.2: 5, 7, 9, 13, 15, 16, 17, 18, 20, 22, 23, 25 and 29. Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• Work practice exercises on Section 3.3 on WeBWorK. Read the definitions carefully! There are several questions that only allow one submission! This is due Wednesday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Read Section 3.5 (pages 163-168). Then complete the Reading Assignment for that section on this handout. Copies of this can be found in the box outside my office. Expanding our abilities to differentiate more functions, we discover how to differentiate trigonometric functions. This reading discusses some special limits involving $\sin x$ and $\cos x$. Then we use these special limits to derive the formulas for the derivatives of trigonometric functions using the definition of the derivative. Since the other four trigonometric functions can be written in terms of $\sin x$ and $\cos x$, the derivatives of the rest can be determined using the quotient rule. Combining these new formulas with our product and quotient rules increases the number of functions we can now differentiate by A LOT!!! Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Wednesday at the beginning of class. It will be considered late if it is turned in after the beginning of class.
• As we start to learn more derivative formulas and special limits, I highly recommend that you make flashcards to help remember them!

Homework due Friday, March 2:

• Rework the problems from the first exam. If you would like a blank copy, come to my office and I will provide you with one. Make sure these questions make sense and that you understand the concepts! If you earned less than 80 out of 114, be sure to come to office hours this week or early next. Everyone is encouraged to stop by to discuss the exam and any questions you have!
• Review the exercises and other notes from Wednesday's class. Recall that the exercises we worked on in group work included: 25, 30, 32, 38a, 41, 45, 49, 51, 55 and 71 from Section 3.3. Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• Work practice exercises on Section 3.4 on WeBWorK. Read the definitions carefully! This is due Friday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Complete the Main Exercises Assignment for Week 7 on this handout. This is due Friday at the beginning of class.
• Want to earn some extra points for your WeBWorK score? Work these BONUS exercises on Section 3.3 on WeBWorK. Read the definitions carefully! This is due SUNDAY at 5:00pm online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Guess what? NO Reading Assignment due Friday! Reread sections 3.4 and 3.5 and solidify this material, letting me know if there are specific questions you would like to discuss! If you feel like looking ahead, check out Section 3.7. The reading assignment for Section 3.7 will be due on Monday.

### WEEK 6: February 19 - February 23

Homework due Monday, February 19:

• Review the group work and notes from Friday's class. If you were not in class, be sure to get notes from someone!!! Recall that we worked on Section 2.5: 11, 19, 41, 43, 47, 51, 53, 57, 59, 67 and 68. Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• No Lab due this Monday!
• Work practice exercises on Sections 2.5 and 2.6 on WeBWorK. Read the directions and hints carefully BEFORE submitting! Remember that you can preview your work before you submit it! This will help to avoid using incorrect notation or autofill. This is due Monday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• NEW CHAPTER!!! Read Section 3.1 (pages 98-108). Then complete the Reading Assignment for that section on this handout. Copies of this can be found in the box outside my office. We have talked about the idea of the slope of the tangent line several times before in class. Now we will get to start calculating it using the formula we derived at the beginning of Chapter 2. Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Monday at the beginning of class. It will be considered late if it is turned in after the beginning of class.

Homework due Wednesday, February 21:

• Review the notes from Monday's class. Make sure that the examples that we worked through make sense, and write down any questions you have. Bring your questions to class or office hours!
• In class we discussed finding the intervals of continuity for the function $f(x)=\frac{e^x}{x}$. We will discuss the function $k(x)=|\ln x|$ on Wednesday. Make an outline of which theorems we need to use in order to justify our interval(s) and work on how to link them all together. Be ready to share your work during full class discussions.
• Work practice exercises on Section 2.6 on WeBWorK. Read the definitions carefully! There are several questions that only allow one submission! This is due Wednesday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Read Section 3.2 (pages 136-141). Then complete the Reading Assignment for that section on this handout. Copies of this can be found in the box outside my office. What is the relationship between continuity and differentiability? If I know what the graph of a function looks like, do I have enough information to graph the derivative function? We will explore these ideas and more in this section, focusing more on the graphical representation of functions and their derivatives rather than their algebraic expressions. Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Wednesday at the beginning of class. It will be considered late if it is turned in after the beginning of class.

Homework for lab on Thursday, February 22:

• Review how the formulas for the different definitions of the derivative are derived. We talked about this back in Section 2.1. In Section 3.1 some good figures to look at are Figure 3.3 and Figure 3.6. If you replace $a$ with $x$ in Figure 3.6, you will see how we get the formula for the definition on page 130.
• Decide how comfortable you feel with this and EMAIL me by 9am on Thursday if you would like us to review any of these derivations. I am happy to do it if anyone needs it!
• At the end of class we started looking at the function $f(x)=\frac{1}{\sqrt{x}}$. At the beginning of lab we will discuss this. Prepare the following: (a) Find the derivative of $f$ at $x=4$ using the formula on page 127. (b) Find the derivative of $f$ as a function using the formula on page 130. I will be looking for volunteers to put these on the board!

Homework due Friday, February 23:

• In class on Wednesday we did this example. Review it and make sure you understand the goals for the solution and why we needed each step.
• Review the exercises and other notes from Wednesday's class. Recall that the exercises we worked on in group work included: 23, 39, 41, 63 and 55 from Section 2.6. Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• Some other good practice problems from Section 2.6 include: 57, 65, 79, 85 and 95-101 odd.
• Work practice exercises on Section 2.6 and Section 3.1 on WeBWorK. Read the definitions carefully! There are questions about continuity, limits of transcendental functions, the Intermediate Value Theorem, and the definition of the derivative. This is due Friday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Complete the Main Exercises Assignment for Week 6 on this handout. This is due Friday at the beginning of class.
• Read Section 3.3 (pages 144-150). Then complete the Reading Assignment for that section on this handout. Copies of this can be found in the box outside my office. It is important to know where the definition of the derivative comes from - DON'T FORGET IT! However, it can be used to prove short-cuts to finding the derivative so that we don't have to calculate limits every time we want to know a derivative. We STILL need to know the definition though (including for your next exam!) -- it is important for our understanding of what the derivative is. Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Friday at the beginning of class. It will be considered late if it is turned in after the beginning of class.

### WEEK 5: February 12 - February 16

Remember that our first exam is Thursday, February 15th in lab. I will post a review sheet on Monday or Tuesday. The exam will cover sections 1.1-1.4, 2.1-2.5 and 2.7.

Here is the Lab Key for the Week 3 Lab. Be sure to read it to make sure the material makes sense and let me know if you have any questions. Also note the level of detail that is necessary for complete solutions.

Homework due Monday, February 12:

• Review the notes from Friday's class. Recall that we worked on Section 2.3: 24, 31, 34, 36, 43, 57b, 59, 69, 89 and also evaluating $\lim_{x\to 0}\Big(5x^4\cos\frac{1}{x}-6\Big)$. Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• Week 4 Lab is due at the beginning of Monday's class! One from each group. Be sure you meet with your group to review each other's final write-ups prior to Monday's class, so that everyone agrees that each group member's set of solutions is a good one. I will roll the die to see which group member will turn in her/hir/his paper. Be sure you send your lab to class with someone else if there is a reason you cannot be there!!!
• If you haven't already, start reviewing for Exam 1. Make yourself a review sheet! I will provide one for you as well, but you will get more out of making one than reading one! Make one now and then compare it to the one I give you early in the week.
• Work practice exercises on Sections 2.3 and 2.4 on WeBWorK. Note that Question 3 only allows ONE submission, not the thirteen tries you normally get. Read the definitions carefully! This is due Monday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Guess what? NO Reading Assignment due Monday! Reread sections 2.3 and 2.4 and solidify material from Section 2.3 and gather questions from Section 2.4. Let me know if there are specific questions you would like to discuss! If you feel like looking ahead, check out Section 2.6. The reading assignment for Section 2.6 will be due on Wednesday.

Since we have an exam this week, there will be NO Main Exercises assignment due on Friday!

Homework due Wednesday, February 14 (Happy Valentine's Day!):

• Review the groupwork exercises and notes from Monday's class. Recall that we worked on Section 2.6: 1, 5, 7, 9, 11, 13, 14, 15, 17, 19, 23 and 24. Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• Work practice exercises on Section 2.3 and 2.4 on WeBWorK. Read the definitions carefully! There are several questions that only allow one, two or three submissions! This is due Wednesday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Work practice exercises on Section 2.4 and 2.5 on WeBWorK. Read the definitions carefully! There are several questions that only allow one or three submissions! This is due Wednesday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Review for the exam. Check out the Review sheet here. Be sure to bring questions to class!
• Email me if there are particular types of questions you would like to see discussed in class.

Homework due Thursday, February 15:

• Prepare for Exam 1! Have confidence in your abilities!!!
• Here is the Lab Key for the Week 4 Lab. Be sure to read it to make sure the material makes sense and let me know if you have any questions. Also note the level of detail that is necessary for complete solutions.
• Arrive on time to lab in Gulick 2000. Remember that seating is assigned randomly, so wait until you are told where to sit.
• You may want to check out some of the practice suggestions and WeBWorK due on Friday for extra practice for the exam.

Homework due Friday, February 16:

• Review the exercises and notes from Wednesday's class. Recall that the exercises we worked on in group work included: (i) Evaluate $\lim_{x\to 0}\Big(8x^6+2x^2\sin\frac{3}{x}-28\Big)$; (ii) Evaluate $\sec($arcsin$\frac{x}{2})$, $\sin($arcsin$\frac{3}{2})$, and arcsin$(\sin\frac{3\pi}{4})$; (iii) 15, 23, 31, 43 and 47 from Section 2.4; and (iv) 23, 27, 29 and 33 from Section 2.5. Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• Work practice exercises on Sections 2.4 and 2.5 on WeBWorK. BE SURE TO DO THEM IN ORDER!!! There are several questions that only allow one or three submissions! PREVIEW YOUR ANSWERS BEFORE SUBMITTING THEM in order to find errors that you can change before submission! Read the directions and hints carefully! This is due Friday at 11:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Recall: THERE IS NO MAIN EXERCISES ASSIGNMENT DUE THIS WEEK!!! :)
• Guess what? No Reading Assignment due on Friday either! :)

### WEEK 4: February 5 - February 9

Here is the Lab Key for the Week 2 Lab. Be sure to read it to make sure the material makes sense and let me know if you have any questions. Also note the level of detail that is necessary for complete solutions.

Homework due Monday, February 5:

• Review the notes from Friday's class. Make sure that the examples that we worked through make sense, and write down any questions you have. Bring your questions to class or office hours!
• Week 3 Lab is due at the beginning of Monday's class! One from each group. Be sure you meet with your group to review each other's final write-ups prior to Monday's class, so that everyone agrees that each group member's set of solutions is a good one. I will roll the die to see which group member will turn in her/hir/his paper. Be sure you send your lab to class with someone else if there is a reason you cannot be there!!!
• Work practice exercises on Section 2.7 on WeBWorK. Note that Question 3 only allows ONE submission, not the thirteen tries you normally get. Read the definitions carefully! This is due Monday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Read Section 2.4 in the text (pages 79-85). Then complete the Reading Assignment for that section on this handout. Copies of this can be found in the box outside my office. What does it mean when the limit of a function goes to infinity? Find out in these pages of the text! See what these infinite limits have to do with vertical asymptotes! Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Monday at the beginning of class. It will be considered late if it is turned in after the beginning of class.

Due to a meeting, my office hours on Wednesday this week are 1:25-1:55pm and 3:15-4:15pm. Contact me if you cannot make those times and have questions.

Homework due Wednesday, February 7:

• Review the groupwork exercises and notes from Monday's class. Recall that we worked on Section 2.7: 7, 11, 16, 19, 20 and also proving that $\lim_{x\to -2}(3x+7)=1$. Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• At the end of class we discussed one trick for solving limits to which we could not just apply Theorem 2.4 and the Limit Laws. The trick we discussed was "Factor and Cancel". Come up with three more tricks that can help us! One trick is explicitly in the reading for Section 2.3. The other two tricks are other kinds of algebraic manipulation (take a look at exercises 64 and 65 on page 78 for ideas). Be ready to share your thoughts in class on Wednesday!
• Work practice exercises on Section 2.3 on WeBWorK. Read the definitions carefully! This is due Wednesday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Guess what? NO Reading Assignment due Wednesday! Reread sections 2.7 and 2.3 and solidify this material, letting me know if there are specific questions you would like to discuss! If you feel like looking ahead, check out Section 2.5. The reading assignment for Section 2.5 will be due on Friday.

Homework due Friday, February 9:

• Review the exercises and notes from Wednesday's class. We did not have a chance to discuss the group work questions as a whole, so if there were some particular ones you want to be sure we discuss on Friday, be sure to let me know if you haven't already. We will look at some that were on the board on Wednesday in addition to some new ones. Recall that the exercises we worked on in group work from Section 2.3 included: 7, 16, 24, 27, 31, 34, 41, 43, 47, 51, 64 and 65. Take special note of question 34 with the one-sided limits. Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• Work practice exercises on Section 2.3 on WeBWorK. Read the definitions carefully! This is due Friday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Complete the Main Exercises Assignment for Week 4 on this handout. This is due Friday at the beginning of class.
• Read Section 2.5 (pages 88-96). Then complete the Reading Assignment for that section on this handout. Copies of this can be found in the box outside my office. Limits at infinity help us understand the end behavior of functions, that is, what happens to the function for very large or very large negative values of $x$. Does the function approach a particular value? Does it tend toward infinity? Does it oscillate? In this section we investigate how to evaluate these limits. This gives us a greater understanding of the function and also will help us graph the functions. Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Friday at the beginning of class. It will be considered late if it is turned in after the beginning of class.

### WEEK 3: January 29 - February 2

Here is the Lab Key for the Week 1 Lab. Be sure to read it to make sure the material makes sense and let me know if you have any questions. Also note the level of detail that is necessary for complete solutions.

Homework due Monday, January 29:

• Review the groupwork exercises and notes from Friday's class. Recall that we worked on Section 1.4: 11, 35, 42, 45, 53, 61, 62 and 79 (as well as some other problems from Wednesday's class). Do more practice problems if necessary until you are confident with all the material!
• Week 2 Lab is due at the beginning of Monday's class! One from each group. Be sure you meet with your group to review each other's final write-ups prior to Monday's class, so that everyone agrees that each group member's set of solutions is a good one. I will roll the die to see which group member will turn in her/hir/his paper. Be sure you send your lab to class with someone else if there is a reason you cannot be there!!!
• Work practice exercises on Section 2.1 on WeBWorK. The second question is a review of algebra and something that will come in handy in Section 2.3! Read the definitions carefully! This is due Monday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Work a practice exercise on Section 2.2 on WeBWorK. Read the definitions carefully! This is due Monday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Read Section 2.7 in the text (pages 112-117). Then complete the Reading Assignment for that section on this handout. This is very theoretical material and can be challenging. Don't let the Greek letters scare you, they are cool and just represent unknown constants. Remember the hand-wavy definition of a limit that we discussed at the end of class on Friday? We want to make that more exact, and that is what is happening in this section. Feel free to review your definitions of absolute values on your green prerequisites sheet if you feel absolute values are causing you confusion here. Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Monday at the beginning of class. It will be considered late if it is turned in after the beginning of class.

Homework due Wednesday, January 31:

• Come to office hours! There will be no more group meetings during office hours so they are completely open for you to come and ask questions! No appointments are necessary for my posted hours! It would be great to have students in every office hour!
• If you forgot to bring your picture to your small group meeting, be sure to bring your picture to class! Remember that this is an assignment and to get full credit, you must submit a picture. (See the end of the syllabus for details.)
• Review the groupwork exercises and notes from Monday's class. All our work was on the handout. Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• There are two SHORT problem sets on WeBWorK. Work practice exercises on Section 2.2 here and here. Read the definitions carefully! This is due Wednesday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Guess what? NO Reading Assignment due Wednesday! Reread sections 2.2 and 2.7 and solidify this material, letting me know if there are specific questions you would like to discuss! If you feel like looking ahead, check out Section 2.3 (we will be jumping back). The reading assignment for Section 2.3 will be due on Friday.

Reminder: Office hours on Thursday have been moved from the morning to 4:30-5:15pm. Contact me if you cannot make those times and have questions.

Homework due Friday, February 2:

• LAST CHANCE: If you forgot to bring your picture to your small group meeting, be sure to bring your picture to class! Remember that this is an assignment and to get full credit, you must submit a picture. (See the end of the syllabus for details.)
• Review the exercises and notes from Wednesday's class. Recall that the exercises from Section 2.2 included: 22, 24, 27, 28, 30, 31, 36, 37, 43 and 46. Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• Work practice exercises on Section 2.2 on WeBWorK. Read the definitions carefully! This is due Friday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Complete the Main Exercises Assignment for Week 3 on this handout. This is due Friday at the beginning of class.
• Read Section 2.3 (pages 69-76). Then complete the Reading Assignment for that section on this handout. Copies of this can be found in the box outside my office. In this section we work on some shortcuts to evaluate limits. These shortcuts are legal because they have been proven using methods similar to what you read about in Section 2.7. It makes our lives much easier than having to complete an $\epsilon$-$\delta$ proof every time we need to evaluate a limit! Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Friday at the beginning of class. It will be considered late if it is turned in after the beginning of class.

### WEEK 2: January 22-26

Homework due Monday, January 22:

• Review the groupwork exercises and notes from Friday's class. Recall that we worked on Section 1.1: 19, 39, 49, 56 and 61; and Section 1.2: 17, 19 & 37, 27, 41 and 43. Do more practice problems if necessary until you are confident with all the material!
• Week 1 Lab is due at the beginning of Monday's class! One from each group. Be sure you meet with your group to review each other's final write-ups prior to Monday's class, so that everyone agrees that each group member's set of solutions is a good one. I will roll the die to see which group member will turn in her/hir/his paper. Be sure you send your lab to class with someone else if there is a reason you cannot be there!!!
• BONUS: This is NOT required, but if you need extra practice on the material from Sections 1.1 and 1.2, then you should do it! You get bonus points toward your WeBWorK score for doing it as well! Work practice exercises on Sections 1.1 and 1.2 on WeBWorK. Note that Question 7 only allows TWO submissions, not the thirteen tries you normally get. Read the definitions carefully! This is due Monday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Work practice exercises on Sections 1.2 and 1.3 on WeBWorK. Note that the first two questions only allow THREE submissions and the last only TWO, not the thirteen tries you normally get. Read the definitions carefully! This is due Monday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Read Sections 2.1 and 2.2 in the text (pages 54-65). [I know I said that we wouldn't read two sections again, but Section 2.1 is really just an introduction to Section 2.2; they really could be the same section. AND they are both short!] Then complete the Reading Assignment for those sections on this handout. Yay! Calculus!!! Now we begin the new material! Limits are important in many ways! ALL the main ideas of calculus are described in terms of limits, so it is vital that we understand limits first. We can use graphs, tables and equations to evaluate and understand limits. In these sections we focus on the first two: graphs and tables. The question we ask as we evaluate limits is "what is happening to our $y$-values as our $x$-values approach certain numbers (and sometimes from certain directions)?". Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of each section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Monday at the beginning of class. It will be considered late if it is turned in after the beginning of class.

Homework due Wednesday, January 24:

• If you have met with me in your small group meeting and forgot to bring your picture, be sure to bring your picture to class!
• Review the groupwork exercises and notes from Monday's class. Recall that we worked on Section 1.3: 14, 19, 25, 27, 40, 43, 51, 69, 73 and an extra problem where I asked you to solve $10^{x^2-4}=1$. Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• Work practice exercises on Section 1.3 on WeBWorK. You should have your log rules readily available to help you!!! Note that Questions 5 and 6 only allow TWO submissions, not the thirteen tries you normally get. Read the definitions carefully! This is due Wednesday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Guess what? NO Reading Assignment due Wednesday! Reread sections 1.1-1.4 and solidify this material, letting me know if there are specific questions you would like to discuss! If you feel like looking ahead, check out Section 2.7 (yes, we will be skipping and coming back to Section 2.3 afterwards).

Homework due Friday, January 26:

• If you have met with me in your small group meeting and forgot to bring your picture, be sure to bring your picture to class! If you haven't met with me yet, please come to your appointment or email me if none of the times I offered in class worked for you.
• Review the exercises and notes from Wednesday's class. Recall that the exercises from Section 1.4 included: 19, 27, 31, 35, 39, 42, and 45 and three extra problems where I asked you to evaluate (a) arctan$(\tan\frac{3\pi}{4})$, (b) $\tan($arctan$\frac{\sqrt{2}}{2})$, and (c) $\sin($arcsin $7)$. Let me know which of these questions you would like to discuss in class. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions!
• Work practice exercises on Section 1.4 on WeBWorK. Read the definitions carefully! This is due Friday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Complete the Main Exercises Assignment for Week 2 on this handout. This is due Friday at the beginning of class.
• Reread Sections 2.1 and 2.2. We will discuss this during the second half of Friday's class.
• Read Section 2.7 (pages 112-119). I will not collect a reading assignment for this section until Monday, but it is complicated material and could really use several careful readings!

### WEEK 1: January 16-19

Welcome to Calculus I!!!

Homework due Thursday, January 18:

Although I will not normally assign homework to be due on non-class days, this week we will need to in order to get started and refresh our memories. Please complete the following:
• Orient yourself to WeBWorK, where you will be completing assignments roughly three times a week. Read these pages for instructions about syntax and an introduction to how the system works: WeBWorK Instructions and FAQs, WeBWorK Syntax and List of Functions.
• Read the syllabus (green for Section 2, and blue for Section 3) and the salmon Homework Guidelines. We went through SOME of this in class, but you should read all the details and make sure you don't have any questions about either document. Also be sure to record the exam dates in your personal calendar/planner. Remember there are no make-ups.
• Familarize yourself with this website. Note that there is a link at the top of the page to your syllabus and to the homework guidelines, should you lose the ones I handed out in class. The syllabus has a lot of vital information on it and you will likely want to refer back to it regularly. Also at the top of the page is a link to my grade scale. This will let you know what percentage you need to earn in order to obtain specific grades (although I hope that learning is your ultimate goal, rather than a specific grade). In addition, there are links to our WeBWorK homepage and the websites with instructions and tips for WeBWorK.
• Read Sections 1.1, 1.2 and 1.3 in the text (pages 1-34). Then complete the Reading Assignment for those sections on this handout. Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) Since this is review, you should feel very comfortable with this material. This is due Thursday at the beginning of lab.
• Practice using WeBWorK with the WeBWorKIntro assignment here. This is due Thursday at 10:00pm.
• Review pre-calculus material with the WeBWorK Calculus Prerequisites assignment. This is due Thursday at 10:00pm. (Note that you can see all assigned WeBWorK Homework Sets by logging into the general site and clicking on Homework Sets in the lefthand tool bar. Clicking the above link takes you directly to the Review assignment.)

Homework due Friday, January 19:

• Work practice exercises on Section 1.1 on WeBWorK. Note that Questions 2 and 5 only allow ONE and TWO submissions (respectively), not the thirteen tries you normally get. Read the definitions carefully! This is due Friday at 10:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Read Section 1.4 in the text (pages 38-47). Then complete the Reading Assignment for that section on this handout. Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) Since this is review, you should feel very comfortable with this material. This is due Friday at the beginning of class.
• Review the green prerequisites sheet you received in class on Wednesday. Work through the group work exercises also distributed on Wednesday. Do you feel comfortable with interval notation?

Hobart and William Smith Colleges: Department of Mathematics and Computer Science
Erika L.C. King