Math 130-03, Spring 2001 Information for the First Test ----------------------------------------------------------------------------- The first test in this course takes place in class on Friday, February 16. It covers Chapter 1, Sections 1 to 6; Chapter 2, Sections 1 and 2; and the first three labs. Here is a list of some of the most important terms and ideas that you should know for this test: Calculus as the study of change Calculus as the study of infinity Function The notation f(x) Functions can be defined by graphs, formulas, or tables of values What does it mean to say "y is a function of x"? Independent variable Dependent variable Real-valued function of a real variable Graph of a function Domain of a function Range of a function The natural domain of a formula The absolute value function The function trunc(x) Computer-generated graphs and their inaccuracies Sampling error Operations on functions: f+g, f-g, fg, f/g Scaling operations (stretching and compressing): f(k*x), k*f(x) Translations: f(x+k), f(x)+k Composition of functions: f(g(x)) Even functions: f(-x) = f(x), symmetry about the vertical axis Odd functions: f(-x) = -f(x), Symmetry about the origin The previous six items, using graphs rather than formulas! Linear function Slope of a line Slope-intercept form of the equation of a line: y = mx + b Point-slope form of the equation of a line: (y - y1) = m(x - x1) Parallel lines Mathematical modeling Polynomial functions Rational functions Asymptotes Trigonometric functions: sin(x), cos(x), tan(x), cot(x), sec(x), csc(x) Definition of sin(x) and cos(x) in terms of the unit circle Radial measure of angles Limits One-sided limits (from left or right) Limits at infinity Infinite limits Reading limits from graphs Limits of formulas Limits and horizontal asymptotes Limits and vertical asymptotes How can a limit fail to exist? Tangent lines Secant lines Slope of a tangent line as a limit of slope of secant lines How can a tangent line fail to exist at a given point on a graph? The limit theorems (2.2.1 and 2.2.2 in the text, pages 128-129) Using the limit theorems to compute limits Limits of rational functions