The following problems from your textbook (Calculus, Early Transcendentals 9E by James Stewart) will be discussed in your discussion sessions. Solutions are provided in your book; please do not refer to them before attempting the problems. I will write some notes in some problems for you and your TA. Enjoy learning! L.V.A
Week 1: Main goal. Exponential function and its inverse(Logarithmic functions)
Section 1.4. Problems 3, 9, 15, 17, 19. (Basic transformations of exponential functions and the domain of the combination of exponential functions and power functions)
Section 1.5. Problems 1, 17, 21 ( Think also of the domain of the function and its inverse), 25, 41, 43, 45 ( The last 3 problems are about the properties of the logarithmic functions )
Week 2: Secant line, average velocity as the approximation of the instantaneous velocity. Introduction to limits: understand the concept of limits.
Section 2.1: 1, 3, 5, 7 ( Secant line, average velocity as the approximation of the instantaneous velocity)
Section 2.2: 1, 5, 7, 17, 19, 21, 29, 31. (This set of problems must be done on Thursday; please bring a calculator.)
Week 3: Vertical asymptotes, using the limit laws to find limits, rationalization method, squeeze theorem
Section 2.2: 33, 35, 43, 47 (Functions that grow without bound)
Section 2.3: 11, 23, 25, 29, 39, 43, 45, 47, 51. (Limit laws, rationalization method, and squeeze theorem)
Week 4: Continuity of a function at a point. Limits at infinity and horizontal asymptotes. Derivatives and rates of change.
Section 2.5 19, 21, 25, 37. (Continuity concept )
Section 2.6: 15, 17, 19, 25, 35, 47. (Limits at infinity)
Section 2.7: 13, 15, 43, 47 (Rates of change)
Week 5: Definition of derivative. Differentiating functions.
Section 2.8: 3, 13, 21, 23, 39. (Matching function with its derivatives, using the definition of derivative, meaning of the derivative as an instantaneous rate of change)
Section 3.1: 17, 19, 23, 31, 67, 71. (Applying the rules of differentiation for exponential and power functions)
Section 3.2: 7, 9, 19, 23, 43 (Product and quotient rule)
Section 3.3: 3, 9, 13, 39, 41, 43. (Product and quotient rule involving trig functions, limits of trigonometric functions)
Week 6: Chain rule. Implicit differentiation. Derivatives of logarithmic functions.
Section 3.4: 9, 13, 35, 39, 47, 59, 65 (This is fun!)
Section 3.5: 5, 7, 25, 31 (Implicit differentiation)
51, 59 (Derivatives of the trig inverse functions)
Section 3.6: 9, 17, 25, 43, 47 (Derivatives of Logarithmic functions)
Week 7: Related rates and linear approximation.
Section 3.9: 1, 3, 5, 7, 13, 15, 29, 33.
Section 3.10: 11, 13, 15, 17, 25, 27. (Using linear approximation to a given number)
Week 8: Review for exam 1 and finding critical points
Tuesday: Review for exam 1. TAs, please cover the following topics:
Differentiable rules. Product, quotient, and chain rules. Implicit differentiation. You must know how to differentiate all the trigonometric functions, the arccosine, arcsine, arctan, logarithmic, exponential, and polynomial functions. Make sure you also know when a function has a tangent line at a point.
Thursday:
Section 4.1: 29, 37, 41, 43 (Only find critical points).
I will cover in class a review of the limits, continuity, differentiability, related rates, and linear approximation.