Calculus Concepts And Contexts 4th Edition By James Stewart – Test Bank

Calculus Concepts And Contexts 4th Edition By James Stewart – Test Bank Sample Questions Section 3.4: The Chain Rule 1. Find the derivative of . a. e. b. f. c. g. d. h. None of these ANS: A PTS: 1 2. Find the derivative of . a. e. b. f. c. g. d. h. None of these ANS: D PTS: 1 3. Find the derivative of . a. e. b. f. c. g. d. h. None of these ANS: F PTS: 1 4. Find the derivative of a. 0 e. 16 b. 28 f. 24 c. 4 g. 12 d. 32 h. 8 ANS: A PTS: 1 5. If a. e. b. f. c. g. d. h. None of these ANS: C PTS: 1 6. If a. 4 e. b. f. c. 12 g. 6 d. 3 h. None of these ANS: E PTS: 1 7. If a. e. b. f. c. g. d. h. 1 ANS: A PTS: 1 8. Let Find the value of a. 2e e. b. e f. c. g. d. h. ANS: E PTS: 1 9. Let Find the value of a. 2 e. b. 4 f. c. 6 g. d. 8 h. ANS: F PTS: 1 10. Let where g is differentiable. Find a. e. b. f. c. g. d. h. ANS: E PTS: 1 11. Suppose that and , Find the value of a. 4 e. 20 b. 8 f. 24 c. 12 g. 28 d. 16 h. 32 ANS: G PTS: 1 12. Suppose that and , Find the value of a. 3 e. 12 b. 4 f. 15 c. 7 g. 17 d. 9 h. 20 ANS: E PTS: 1 13. Suppose that and and Find a. 5 e. 25 b. 10 f. 30 c. 15 g. 35 d. 20 h. 40 ANS: D PTS: 1 14. Suppose that , find a. 0 e. 8 b. 2 f. c. 4 g. d. 6 h. ANS: D PTS: 1 15. If a. 4 e. 16 b. 24 f. 8 c. 28 g. 32 d. 12 h. 6 ANS: C PTS: 1 16. If a. e. b. f. c. 1 g. d. h. ANS: A PTS: 1 17. If a. e. b. f. c. g. d. h. c. g. 19. If where k is a constant. a. e. b. f. c. g. d. h. ANS: E PTS: 1 20. Find the y-intercept of the tangent line to the curve at the point (1, 2). a. e. b. f. 1 c. g. d. 2 h. ANS: B PTS: 1 21. Find the slope of the tangent to the curve when a. e. b. f. c. g. d. h. ANS: C PTS: 1 22. Find the slope of the tangent to the curve , when a. e. 3 b. f. c. g. d. h. 4 ANS: H PTS: 1 23. At what value of t does the curve have a vertical tangent? a. e. b. f. c. g. d. h. ANS: A PTS: 1 24. Find the slope of the tangent to the curve when . a. e. b. f. c. g. 1 d. 0 h. ANS: G PTS: 1 25. Given find the value of when a. e. b. f. 2 c. g. 1 d. h. ANS: E PTS: 1 26. Find the slope of the tangent to the curve with parametric equations at the point (0, 1). a. e. 1 b. f. 2 c. g. 3 d. 0 h. 4 ANS: F PTS: 1 27. Find (a) (b) (c) (d) ANS: (a) (b) (c) (d) PTS: 1 28. Find (a) (b) (c) (d) ANS: (a) (b) (c) (d) PTS: 1 29. Find (a) (b) (c) (d) ANS: (a) (b) (c) (d) PTS: 1 30. Find , (a) (b) (c) (d) ANS: (a) (b) (c) (d) PTS: 1 31. Find . (a) (b) (c) (d) ANS: (a) (b) (c) (d) PTS: 1 32. Suppose that u and v are differentiable functions and that and Find ANS: PTS: 1 33. f and g are functions whose graphs are shown below. Let and Find each derivative, if it exists. If it does not exist, explain. (a) (b) (c) (d) (e) (f) (g) (h) (i) ANS: (a) (b) (c) (d) undefined because does not exist. (e) (f) (g) (h) undefined because does not exist. (i) PTS: 1 34. Suppose that h (x) = f (g (x)) and that we are given the following information: Use the table to estimate the value of (0:3). Justify your estimation. ANS: PTS: 1 35. Find an equation of the tangent line to the curve at the point (1, 8). ANS: The slope is 24, so an equation of the tangent line is PTS: 1 36. Find an equation of the tangent to the curve at . ANS: PTS: 1 37. Find the point where the tangent to the curve has zero slope. ANS: (2, 2) PTS: 1 38. Find the y-intercept of the tangent line to the curve at the point (, 0). ANS: PTS: 1 39. According to the theory of relativity, the mass of an object at speed v is given by where c is the speed of light and is the mass of the object when it is at rest. Find . ANS: PTS: 1 40. The position of a particle moving along the x-axis is given by meters, where t is measured in seconds. (a) Determine the position, velocity, and acceleration of the particle when t = 0.65. (b) Show that the acceleration of the particle is proportional to its position, but in the opposite direction. ANS: (a) ; ; (b) PTS: 1 41. The angular displacement q of a simple pendulum is given by where is the angular amplitude, w the angular frequency and q a phase constant depending on initial conditions. If we are given that w = 10 and , find the angular velocity when . ANS: ; when , so . So . PTS: 1 42. The displacement of a particle is given by . Find all times t 0 where (a) The displacement attains its maximum value. (b) The velocity attains its maximum value. (c) The acceleration attains its maximum value. ANS: (a) . (b) (c) PTS: 1 43. Let be the amount of salt (in kg) in a tank after time t minutes. Find: (a) How much salt is in the tank after 1 hour? (b) Find the rate of change of salt after 1 hour? ANS: (a) . (b) PTS: 1 44. Let be the population of a bacteria colony at time t hours. Find the growth rate of the bacteria after 10 hours. ANS: About 2.7/h PTS: 1 45. Let be the population of a bacteria colony at time t hours. Find the growth rate of the bacteria after 10 hours. ANS: PTS: 1 46. Consider the two functions and (a) Which, if either, of these functions is periodic? Justify your answer. (b) For each function, consider the limit as x increases without bound. Does either function also increase without bound like an exponential function? Explain. (c) Where, if anywhere, does each function have an x-intercept? Justify your answer. (d) Where, if anywhere, does each function have a horizontal tangent line? Justify your answer. (e) Where, if anywhere, does each function attain its maximum value? its minimum value? Justify your answers. ANS: (a) Since is periodic. (b) No, and Both functions are bounded. (c) are x-intercepts of g(x). for all x, so f has no x-intercepts. (d) f(x) has horizontal tangent lines where , g(x) has horizontal tangent lines where , (e) is maximized when that is, when , is maximized when , that is, when , is minimized when that is, when , is minimized when , that is, when , PTS: 1 47. The function f is graphed below. Let and .Use the graph to estimate each of the following. (a) (b) (c) ANS: (a) (b) (c) So PTS: 1 48. Find the derivative if where m and c are constants, v is velocity function. ANS: PTS: 1 49. Consider the curve given by Find at the point corresponding to ANS: PTS: 1 50. Consider the curve given by Find at the point corresponding to ANS: PTS: 1 51. Find an equation in x and y for the tangent line to the curve at the point ANS: PTS: 1 52. Find for the parametric curve given by ANS: PTS: 1 53. Find for the parametric curve given by ANS: PTS: 1 Section 4.2: Maximum and Minimum Values 1. Find all critical numbers for the function . a. 0 e. 8 b. 0, 8 f. 1, –1 c. 0, 4 g. 4 d. No Critical Number h. None of the above ANS: B PTS: 1 2. Find all critical numbers for the function . a. 1 e. 2 b. 1, 2 f. 1, –1 c. –1 g. –1, 2 d. No Critical Number h. None of the above ANS: D PTS: 1 3. Find all critical numbers for the function . a. 0 e. 3 b. –3 f. 3, –3 c. 0, –3 g. 0, 3, –3 d. No Critical Number h. None of the above ANS: G PTS: 1 4. Find all critical numbers for the function . a. 0 e. 3 b. –3 f. 3, –3 c. 0, –3 g. 0, 3, –3 d. No Critical Number h. None of the above ANS: A PTS: 1 5. Find all critical numbers for the function . a. 0 e. 3 b. –3 f. 3, –3 c. 0, –3 g. 0, 3, –3 d. No Critical Number h. None of the above ANS: G PTS: 1 6. Find all critical numbers for the function . a. e. b. f. c. 0 g. 1 d. None of these h. No critical numbers ANS: B PTS: 1 7. Find all critical numbers for the function . a. e. b. f. c. 0 g. 1 d. None of these h. No critical numbers ANS: F PTS: 1 8. Find all critical numbers for the function . a. e. b. f. c. 0 g. 1 d. None of these h. No critical numbers ANS: E PTS: 1 9. Find the minimum value of the function . a. –1 e. b. f. 0 c. g. d. 1 h. ANS: D PTS: 1 10. Find the value x at which the minimum of the function occurs. a. 1 e. 0 b. f. c. g. 1 d. h. ANS: A PTS: 1 11. Find the distance between the two critical numbers of the function . a. 4 e. 2 b. 1 f. 9 c. 8 g. 6 d. 3 h. 5 ANS: E PTS: 1 12. Find the difference between the local maximum and the local minimum values of the function . a. 4 e. 6 b. 1 f. 5 c. 9 g. 8 d. 2 h. 3 ANS: A PTS: 1 13. Find the absolute maximum of the function on the interval . a. e. 1 b. f. c. 0 g. d. h. 2 ANS: H PTS: 1 14. Find the absolute minimum and maximum values of the function on the closed interval . a. 0, 3 e. 3, 16 b. 0, 5 f. 5, 7 c. 3, 5 g. 7, 16 d. 3, 9.75 h. 5, 10.25 ANS: E PTS: 1 15. Find the minimum and maximum values of on the interval . a. e. b. f. c. 0, 8 g. d. h. ANS: B PTS: 1 16. Given that has critical numbers at find a and b. a. 6 e. 9, 3 b. 8, 7 f. 8, 4 c. 7, 8 g. 7, 5 d. 6, 9 h. 6, 6 ANS: D PTS: 1 17. Find the absolute maximum of the function a. e. 2 b. 1 f. c. g. d. h. No absolute minimum ANS: H PTS: 1