College Calculus Final Review
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1 College Calculus Final Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Determine the following limit. (Hint: Use the graph to calculate the limit.) does not exist
2 2. Let Determine the following limit. (Hint: Use the graph to calculate the limit.) does not exist 3. Let and. Find the limit
3 4. Find the following limit (if it exists). Write a simpler function that agrees with the given function at all but one point Find the limit (if it exists) Find the limit (if it exists). 6.
4 7. Use the graph as shown to determine the following limits, and discuss the continuity of the function at. (i) (ii) (iii) 2, 2, 2, 2, 2, 2, 8. Use the graph to determine the following limits, and discuss the continuity of the function at. (i) (ii) (iii)
5 9. Find the limit (if it exists). 10. Find the x-values (if any) at which is not continuous. 11. Find the x-values (if any) at which is not continuous. 12. Find the vertical asymptotes (if any) of the function. 13. Find the derivative of the function.
6 14. Find the derivative of the function. 15. Use the rules of differentiation to find the derivative of the function. 16. Find the slope of the graph of the function at the given valu when
7 17. Find the slope of the graph of the function at the given valu at 18. Find the derivative of the function. 19. Determine all values of, (if any), at which the graph of the function has a horizontal tangent. The graph has no horizontal tangents. 20. Find the derivative of the algebraic function.
8 21. Use the Product Rule to differentiate.
9 22. Use the Quotient Rule to differentiate the function. 23. Find the derivative of the function.
10 24. Find an equation of the tangent line to the graph of f at the given point. 25. The length of a rectangle is and its height is, where t is time in seconds and the dimensions are in inches. Find the rate of change of the area, A, with respect to tim square inches/second square inches/second square inches/second square inches/second square inches/second 26. Find the second derivative of the function.
11 27. Suppose that an automobile's velocity starting from rest is secon Find the acceleration at 9 seconds. Round your answer to one decimal plac 1.9 ft/sec ft/sec ft/sec ft/sec ft/sec 2 where v is measured in feet per 28. Find the derivative of the function. 29. Find the derivative of the function.
12 30. Find the derivative of the function. 31. Find the derivative of the function.
13 32. Find by implicit differentiation. 33. Find by implicit differentiation.
14 34. Find by implicit differentiation. 35. Find an equation of the tangent line to the graph of the function given below at the given point. (The coefficients below are given to two decimal places.) 36. The radius, r, of a circle is decreasing at a rate of centimeters per minut Find the rate of change of area, A, when the radius is. sq cm/min sq cm/min sq cm/min sq cm/min sq cm/min
15 37. A spherical balloon is inflated with gas at the rate of radius of the balloon increasing at the instant the radius is cubic centimeters per minut How fast is the centimeters? 38. A ladder feet long is leaning against the wall of a house (see figure). The base of the ladder is pulled away from the wall at a rate of feet per secon How fast is the top of the ladder moving down the wall when its base is feet from the wall? Round your answer to two decimal places. ft/sec ft/sec ft/sec ft/sec ft/sec 39. Find all critical numbers of the function. critical numbers: critical numbers: critical numbers: critical numbers: no critical numbers
16 40. Identify the open intervals where the function is increasing or decreasing. decreasing: ; increasing: decreasing on increasing: increasing: increasing: ; decreasing: ; decreasing: ; decreasing: 41. Find the open interval(s) on which is increasing or decreasing. increasing on decreasing on increasing on decreasing on increasing on decreasing on increasing on decreasing on increasing on decreasing on
17 42. The graph of f is shown in the figur Sketch a graph of the derivative of f
18 43. Determine the open intervals on which the graph of upwar is concave downward or concave concave downward on concave upward on ; concave downward on concave upward on ; concave downward on concave upward on concave downward on ; concave upward on 44. Find all relative extrema of the function applicabl. Use the Second Derivative Test where relative max: ; no relative min no relative max; no relative min relative min: ; relative max: relative min: ; no relative max relative min: ; relative max: 45. Find the limit
19 46. Find the limit. 1 0 does not exist 47. Find the limit Find the limit. 1 6
20 49. The graph of a function f is is shown below. Sketch the graph of the derivative.
21 50. Find the length and width of a rectangle that has an area of 968 square feet and whose perimeter is a minimum. 51. Find the indefinite integral.
22 52. Find the indefinite integral. 53. Find the indefinite integral of the following function and check the result by differentiation.
23 54. Solve the differential equation.
24 College Calculus Final Review Answer Section MULTIPLE CHOICE 1. D 2. C 3. B 4. B 5. A 6. D 7. A 8. C 9. D 10. D 11. A 12. B 13. E 14. D 15. C 16. D 17. A 18. B 19. A 20. D 21. D 22. A 23. B 24. C 25. C 26. C 27. B 28. B 29. B 30. E 31. C 32. D 33. A 34. B 35. C 36. C 37. C 38. C 39. B 40. D 41. E
25 42. C 43. D 44. D 45. E 46. D 47. C 48. B 49. B 50. B 51. E 52. B 53. B 54. E
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