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.
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 and 19, 21, 29, 31. (Please bring a calculator for these last 4 problems.)
Week 3: Vertical asymptotes, using the limit laws to find limits, rationalization method.
Section 2.2: 33, 35, 43, 47 (Functions that grow without bound)
Section 2.3: 11, 23, 25, 29, 43, 47, 49, 51 (Limit laws, rationalization method)
Week 4: Squeeze theorem. Continuity of a function at a point. Limits at infinity and horizontal asymptotes. Derivatives and rates of change.
Section 2.3: 39, 41. (Squeeze Theorem)
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 functions with their derivatives, using the definition of the 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)
Quiz 1
Week 6: Product and quotient rule. Chain rule.
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)
Section 3.4: 9, 13, 35, 39, 47, 59, 65 (This is fun!)
Week 7: Chain rule. Implicit differentiation. Derivatives of logarithmic functions.
Section 3.4: 45, 51, 53, 57, 65.
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 8: 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.
Week 9: Linear approximation.Finding the absolute max and min. Mean Value Theorem.
Section 3.10: 33
Section 4.1: 47, 51, 57, 71, 73
Section 4.2: 1, 7, 15.
Quiz 2
Week 10: The first derivative test. Concavity. Inflection points. L'Hôpital's Rule
Section 4.3: 37, 49, 75 (This is a nice problem to see the meaning of inflection points.)
Section 4.4: 1, 15, 21, 27, 41, 51, 55, 63
Section 4.5: 15, 17
Week 11: Optimization problems and antiderivatives.
Section 4.7: 5, 9, 13, 37
Section 4.9: 3, 7, 13, 17, 41, 61
Quiz 3
Week 12: Properties of definite integrals.
Section 5.1: 5, 11.
Section 5.2: 7, 35, 51, 57.
Review for Exam 2 (Anything that you and your TA want to discuss from the list of topics for Exam 2).
In class on Tuesday (Nov. 10), I will focus on reviewing related rates, L'Hôpital's, and optimization.