# MATH 130 - Spring 2019 Calculus I

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

Office Hours: M 1:30-2:30pm, W 1:30-3:00pm, Th 3:30-4:30pm, F 9:30-11:00am, and by appointment

Class: MWF 12:20-1:15pm in Eaton 111
Lab: Th 1:30-2:55pm in Gulick 2000

Course Syllabus

Course Prerequisites
Course Homework Guidelines

Math Intern Hours with Drew Scammell in Lansing 310: Su: 4:00-6:00pm and 7:00-10:00pm; M-Th 3:00-6:00pm and 7:00-10:00pm

### WEEK 9: March 25 - March 29

Have a great spring break!!!

Due to an appointment on Monday afternoon, my Monday office hours will be moved to Tuesday for this week. My hours will be Tuesday, March 26th, 1:00pm-2:00pm. My hours for the rest of the week (Wednesday, Thursday and Friday) will be normal.

Remember that our second exam is Thursday, March 28th in lab. The exam will cover sections 2.5, 2.6, 3.1-3.5, 3.7 and 3.8.

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 25:

• 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!
• There are optional bonus problem sets due on Tuesday that involve composition of functions and the chain rule. (See below.) You may want to complete these before you complete the set due on Monday.
• 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 11:00am 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 9 on this handout. This is due Monday at 12:20pm. It will be considered late if it is turned in after the beginning of class.
• Read Section 3.9 (pages 208-215). 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 12:20pm. It will be considered late if it is turned in after the beginning of class.

BONUS! Want some extra practice with compositions of functions? Try these problems on WeBWorK. Read the directions carefully! This is due TUESDAY, March 26 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 TUESDAY, March 26 at 6:00pm online.

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.

Homework due Wednesday, March 27:

• Review the groupwork exercises and notes from Monday's class. Recall that we worked on Section 3.8: 17, 20, 31, 32, 33, 38, 39, 51 and 53. Everyone seemed pretty confident with those questions. In round two of board work questions we were working on Section 3.8: 47, 45, 49, 55, 59, 57, 65, 87 and 89. Be sure that you take time to look over this second set especially and 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 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 11:00am 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 218-224). 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 12:20pm. 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 on Wednesday.

### WEEK 8: March 11 - March 15

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 11:

• Review the group work and notes from Friday's class. Recall that we worked on Section 3.4: 13, 15, 33, 37, 45, 69, 71, 55, 79, 63, 65 and 91. 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 on the last example we put on the board. Be sure to check out the other trick (we discussed but didn't write) with limits in Example 1b on pages 164-165! (Dividing the numerator and denominator by $x$!)
• 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 11:00am 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 Monday at 12:20pm. It will be considered late if it is turned in after the beginning of class.
• Read Section 3.7 (pages 191-196). 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 12:20pm. It will be considered late if it is turned in after the beginning of class.

Homework due Wednesday, March 13:

• 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 70 points on the exam!
• Review the groupwork exercises and notes from Monday's class. Recall that we worked on Section 3.5: 11-21. Especially take the time to work through Exercise 18! 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!
• We used the special trigonometric limits to help us prove formulas for derivatives of trigonometric functions. Now work practice exercises on those 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 11:00am 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 201-204). 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 12:20pm. 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 15:

• Remember: If you earned less than 70 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 70 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: 27, 29, 52, 48, 59, 62, 65, 37, 75a, 77, 78 and 68 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!
• During lecture we discussed two questions that you are to prepare for Friday's class. The first is to find the derivative of $f(x)=\frac{6}{x^3+e^x}$ using the quotient rule, and check to see if it matches our result for the derivative when we rewrote the function first and then used the chain rule. The second was to find the derivative of the function $k(x)$ that is found in question 4 on your reading assignment for Section 3.7.
• 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 11:00am 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 11:00am 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 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, March 25, after spring break, together with the usual Monday Main Exercises assignment.

### WEEK 7: March 4 - March 8

Homework due Monday, March 4:

• Review the group work and notes from Friday's class. Recall that we worked on Section 3.1: 23, 27, 29, 31, 39, 41, 45, 51, 56 and 60. 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 3.2 on WeBWorK. Make sure you use a computer that has an updated version of Adobe Flash. You will need it for the first question. 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 11:00am 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 163-167). Then complete the Reading Assignment for that section on this handout. Copies of this can be found in the box outside my office. In Section 3.3 you read about 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 12:20pm. It will be considered late if it is turned in after the beginning of class.
• Complete the Main Exercises Assignment for Week 7 on this handout. Remember that this should look more like an essay than you are used to for mathematics problems. This is due Monday at 12:20pm. It will be considered late if it is turned in after the beginning of class.

Homework due Wednesday, March 6:

• Review the groupwork exercises and notes from Monday's class. Recall that we worked on Section 3.2: 23, 25, 27, 29, 37, 43, 47, 52, 60, 18, 54, 56 and 66. 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 11:00am 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 171-175). 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 12:20pm. 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 8:

• 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 70, 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: 47, 50, 51, 52, 54, 62, 65, 69, 73, 79, 41 and 75 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 11:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• 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.

• THIS IS DUE ON MONDAY: Complete the Main Exercises Assignment for Week 8 on this handout. This is due Monday at 12:20pm. It will be considered late if it is turned in after the beginning of class.

### WEEK 6: February 25 - March 1

Due to visiting another professor's class, my Friday office hours this week will be moved to 1:30-2:30. Let me know if you cannot make my office hours this week and have questions. Plan ahead!

Homework due Monday, February 25:

• Review the group work and notes from Friday's class. Recall that we worked on Section 2.5: 44, 47, 49, 59, 63, 71, 80 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!
• 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 11:00am 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 131-137). 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 12:20pm. It will be considered late if it is turned in after the beginning of class.
• Note that since we have an exam on Thursday, there will be no Main Exercises assignment due on Monday!

Homework due Wednesday, February 27:

• Review the groupwork exercises and notes from Monday's class about different types of discontinuities (see the side bar on page 104). Recall that we worked on Section 2.6: 1, 5, 7, 9, 10, 15, 97-101. 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!
• Reread Section 2.6 and remind yourself what Theorems 2.9, 2.10, 2.11, 2.13 and 2.15 say especially. In class we briefly discussed finding the intervals of continuity for the function $f(x)=\frac{e^x}{x}$ (this was number 15 from group work). Make sure you write down that whole solution and that the process makes sense. 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 11:00am 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 140-148). 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 28:

• Review the group exercises from Wednesday's class. Recall that the exercises we worked on in group work included: 27, 39, 43, 71, 65, 73, 87 and 69 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!
• Prepare your group's question from Wednesday's group work. The groups who worked on problems 27, 43 (there were two groups working on this -- work together to do the best possible solution!) and 87 should put their solutions on the board as soon as they arrive in lab. If another group wants to discuss their problem, go ahead and put that on the board as well. Everyone should be ready to put their solutions on the board in case another group requests to discuss their question.
• Bring your reading worksheet from Section 3.1 to lab! We will discuss this section after we finish with the group work examples and before we move into general lab group work.
• Review how the formulas for the different definitions of the derivative at a point 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, Figure 3.5, and Figure 3.8.
• We will do an example to discuss Section 3.1 using the function $f(x)=\frac{1}{\sqrt{x}}$. Try applying both definitions of the derivative of a function at a point (found on page 135) to this function $x=4$. I will be looking for volunteers to put these on the board!

Homework due Friday, March 1:

• 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 your notes on the Intermediate Value Theorem as well!
• 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. You may want to wait until after lab on Thursday to do questions 7-10. 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.
• Read Section 3.3 (pages 152-159). 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 12:20pm. It will be considered late if it is turned in after the beginning of class.

• THIS IS DUE ON MONDAY: Complete the Main Exercises Assignment for Week 7 on this handout. This is due Monday at 12:20pm.

### WEEK 5: February 18 - February 22

Remember that our first exam is Thursday, February 21st 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.

Homework due Monday, February 18:

• Review the notes and group work from Friday's class. Recall that we worked on Section 2.3: 76, 89, 83(b), 71 and also evaluating $\lim_{x\to 0}\Big(5x^4\cos\frac{1}{x}-6\Big)$, $\lim_{x\to 0}\Big(8x^6+2x^2\sin\frac{3}{x}-28\Big)$, $\lim_{x\to 4}\frac{x-4}{\sqrt{x}-2}$, and $\lim_{x\to 4}\frac{x^2-16}{\sqrt{x}-2}$. 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 the class we started an example of looking for the vertical asymptotes of a rational function. Check the second possible $x$ value and come to class ready to argue that it is or is not a vertical asymptote on Monday.
• 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 11:00am 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 5 on this handout. This is due Monday at 12:20pm.
• 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.

Homework due Wednesday, February 20:

• Review the notes from Monday's class. Review Example 3 on pages 95-96 in the text, and also Theorem 2.7. How can Theorem 2.7 give you a shorter way to answer the limits in Example 3?
• Work practice exercises on Section 2.3 and 2.4 on WeBWorK. Read the definitions carefully! Different questions require different notation!!! There are several questions that only allow one, two or three submissions! This is due Wednesday 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.
• 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 11:00am 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.

Lab Key: Would you like to check your answers and work on the Week 4 Lab? Would you like to see if you are skipping any steps when working through a question? Check out the key below! Note how detailed solutions are!

Due to an appointment, my Friday office hours this week will be moved to 1:30-2:30. Let me know if you cannot make those and have questions.

Homework due Thursday, February 21:

• Prepare for Exam 1! Have confidence in your abilities!!!
• Arrive on time to lab in Gulick 2000. Remember that seating is assigned randomly, so wait until the signs are out to find your place 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 22:

• Review the exercises and notes from Wednesday's class. Here are some practice problems: Section 2.4: 17, 27, 47, 57 and 61; Section 2.5: 7, 17, 39, 41 and 43. 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.
• Guess what? No Reading Assignment due on Friday!

• Note that since we have an exam on Thursday, there will be no Main Exercises assignment due on Monday!

### WEEK 4: February 11 - February 15

Homework due Monday, February 11:

• 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!
• Complete the Main Exercises Assignment for Week 4 on this handout. This is due Monday at 12:20pm.
• Work practice exercises on Section 2.7 on WeBWorK. Note that Question 1 only allows ONE submission, not the thirteen tries you normally get. Read the definitions carefully! This is due Monday 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.
• Read Section 2.4 in the text (pages 83-88). 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.

Lab Key: Would you like to check your answers and work on the Week 2 Lab? Would you like to see if you are skipping any steps when working through a question? Check out the key below! Note how detailed solutions are!

Homework due Wednesday, February 13:

• You may recall the first day of class I asked you to check your exam schedule. There are several classmates who have conflicts with the suggested final exam time (using the lab time instead of the class time). Thus we will not be able to move the final exam to the lab time and we will keep it as scheduled through the Registrar during the class time. The syllabus on the website is updated to reflect this change. To make sure that everyone has read this and has put the information in their calendars, I ask that you print out and sign this document. Turn in the signed document on Wednesday. Copies of this can be found in the box outside my office.
• 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 $\lim_{x\to -2}(3x+7)=1$ and $\lim_{x\to -3}(10x+8)=-22$. 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 two tricks for solving limits to which we could not just apply Theorem 2.4 and the Limit Laws. The tricks we discussed were "Factor and Cancel" and "Rationalize and Cancel". Come up with two more tricks that can help us! These tricks are other kinds of algebraic manipulation (take a look at exercises 52 and 53 on page 80 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 11:00am 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 15:

• Review the exercises and notes from Wednesday's class (and Thursday lab!). Recall that the exercises we worked on in group work from Section 2.3 included: 17, 22, 25, 29, 12, 74, 35, 37, 41, 47, 52 and 53. 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 11:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Read Section 2.5 (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.

Lab Key: Would you like to check your answers and work on the Week 3 Lab? Would you like to see if you are skipping any steps when working through a question? Check out the key below! Note how detailed solutions are!

• THIS IS DUE ON MONDAY: Complete the Main Exercises Assignment for Week 5 on this handout. This is due Monday at 12:20pm.

### WEEK 3: February 4 - February 8

Homework due Monday, February 4:

• Review the group worksheet and notes from Friday's class. If your group did not finish the worksheet, make sure you complete it before class on Monday (there are two sides!). Bring questions to class and/or office hours (mine and Drew's)!
• 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 11:00am online. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online.
• Note that there is no Reading Assignment due this Monday!
• Complete the Main Exercises Assignment for Week 3 on this handout. This is due Monday at 12:20pm.

Lab Key: Would you like to check your answers and work on the Week 1 Lab? Would you like to see if you are skipping any steps when working through a question? Check out the key below! Note how detailed solutions are!

Homework due Wednesday, February 6:

• 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. Make sure you have completed the group worksheet from class and let me know if you have any questions about it.
• There are three SHORT problem sets on WeBWorK. Work practice exercises on Section 2.2 here, here and here. Read the definitions carefully! This is due Wednesday at 11:00am online. The last set has some algebra review questions on absolute values that will help us with Section 2.7. 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.

Homework due Friday, February 8:

• LAST CHANCE: If you forgot to bring your picture to your small group meeting, be sure to bring your picture to class (and include your name on it)! 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 about absolute values from Wednesday's class. Recall that the exercises from Section 2.2 included: 18, 33, 46, 48, 49, 50, 51, 35, and 54. 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!
• Answer the first question on the handout we started discussing at the end of class on Wednesday.
• Work practice exercises on Section 2.2 on WeBWorK. Read the definitions 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.
• Read Section 2.3 (pages 71-79). 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.SOME COPIES OF THE READING ASSIGNMENT ARE AVAILABLE IN THE BOX OUTSIDE MY OFFICE

• THIS IS DUE ON MONDAY: Complete the Main Exercises Assignment for Week 4 on this handout. This is due Monday at the beginning of class.

### WEEK 2: January 28 - February 1

Homework due Monday, January 28:

• Review the groupwork exercises and notes from Friday's class. Recall that we worked on Section 1.1: 29, 45, 55 and 67; and Section 1.2: 7, 13, 23, 33, 47, 51 and 53. Do more practice problems if necessary until you are confident with all the material!
• 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). 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 (12:20). It will be considered late if it is turned in after the beginning of class. SOME COPIES OF THE READING ASSIGNMENT ARE AVAILABLE IN THE BOX OUTSIDE MY OFFICE
• Note that there are no Main Exercises due this Monday!

Homework due Wednesday, January 30:

• Review the groupwork exercises and notes from Monday's class. Recall that we worked on Section 1.3: 4, 25, 28, 29, 12, 53, 49, 77, 81 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!!! (They are at the top of page 34 in the margin!) 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 11:00am 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, February 1 (Happy February!):

• 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 exercises and notes from Wednesday's class. Recall that the exercises from Section 1.4 included: 23, 31, 69, 35, 37, 42, 65, 87, 93 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.
• Reread Sections 2.1 and 2.2. We will discuss this during the second half of Friday's class.

### WEEK 1: January 22 - January 25

Welcome to Calculus I!!!

Homework due Thursday, January 24:

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:
• Bring the green prerequisites sheet and the group work exercises you received in class on Wednesday to lab. We will look at these, and you need not finish the sheet before lab.
• Read the syllabus 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. Note that these are both bright colors! That is because they are important and you should refer to them often. 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 1-35). Then complete the Reading Assignment for those sections on this handout. (It is the same handout I gave in class!) 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 (1:30pm).
• 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.
• Review the Prerequisites for MATH 130. This is an outline and you should feel comfortable filling in the details. The information on this sheet is information that you should feel confident using. You will need to apply it regularly in the middle of calculus questions. If you do not feel confident with this material, contact me immediately so that we can discuss whether you need to work on a review or start in another course in order to succeed. A link to this guide is also listed at the top of this website.
• Practice using WeBWorK with the WeBWorKIntro assignment here. This is due Thursday at 12:00pm (Noon).
• Review pre-calculus material with the WeBWorK Calculus Prerequisites assignment. This is due Thursday at 12:00pm (Noon). (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.)
• Fill out this autobiographical questionnaire. Print it two sided if possible. If you can only print one sided, be sure to staple it. If you have any issues printing, let me know ASAP. You must turn in the questionnaire on the handout. Be sure to leave the top portion on the first side (above where you place your name) blank. This is due Thursday at 1:30pm at the beginning of lab.

Homework due Friday, January 25:

• 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 11:00am 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.
• Check your other classes exam schedules and any sports schedules to see if you would have a conflict with our final exam being scheduled during our lab exam time as listed on the syllabus. Let me know ASAP if there is any academic or athletic reason you would have trouble attending that exam.

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