Multiple Choice Indicate the answer choice that best completes the statement or answers the question. 1. Evaluate the given definite integral. 2. Find the derivative of the function. 3. Find the derivative of the function. Copyright Cengage Learning. Powered by Cognero. Page 1
4. Find the derivative of the function. 5. Find the derivative of the function by using the rules of differentiation. 6. Find the slope and an equation of the tangent line to the graph of the function at the point. ; ; ; ; Copyright Cengage Learning. Powered by Cognero. Page 2
7. Let. Find. 8. Find the indefinite integral. 9. Find the indicated limit, if it exists. e. The limit does not exist. 10. Find the indicated limit. e. 11. Find the limit, if it exists. Copyright Cengage Learning. Powered by Cognero. Page 3
e. The limit does not exist 12. Find an equation of the tangent line to the graph of the function at the point. 13. Find the derivative of the function. 14. Find the indefinite integral. Copyright Cengage Learning. Powered by Cognero. Page 4
15. Custom Office makes a line of executive desks. It is estimated that the total cost for making x units of their Senior Executive model is dollars/year. Find the marginal average cost function. 16. Use the laws of logarithms to simplify the expression. 17. A function f is continuous at the point if the following conditions are satisfie 1. is define 2. exists. 3.. Determine the values of x, if any, at which the function is discontinuous. At each point of discontinuity, state the condition(s) for continuity that are violate Copyright Cengage Learning. Powered by Cognero. Page 5
; condition 3 ; conditions 1, 2 ; condition 2 ; conditions 1, 2 e. Continuous everywhere 18. Find the domain of the function. e. 19. Find the domain of the function. Copyright Cengage Learning. Powered by Cognero. Page 6
e. 20. Find an equation of the line in general form that passes through the point (5, 8) and is perpendicular to the line. 49x + 28y = -144 4x + 7y = 36 4x + 7y = -36 4x - 7y = -36 e. 49x - 28y = -144 21. Find the slope of the line that passes through points and. 4 5 1 6 e. 2 22. Find the present value of $20,000 due in 4 year(s) at the given rate of interest. Round your answer to the nearest dollar. 5% / year compounded monthly 8% / year compounded daily $16,381, $14,523 $16,381, $24,418 $16,381, $27,542 $14,523, $24,418 Numeric Response Enter the appropriate value to answer the question or solve the problem. 23. Based on a preliminary report by a geological survey team, it is estimated that a newly discovered oil field can be expected to produce oil at the rate of Copyright Cengage Learning. Powered by Cognero. Page 7
thousand barrels/year, t years after production begins. Find the amount of oil that the field can be expected to yield during the first 14 year(s) of production, assuming that the projection holds true. Please round your answer to the nearest whole number. thousand barrels 24. Find the limit. 25. Find the limit. 26. Suppose a certain economy's consumption function is, where C(x) and x are measured in billions of dollars. Find the marginal propensity to consume (the rate of change of consumption with respect to income, ) when. Round the answer to two decimal places, if necessary. $ billion/billion dollars 27. Let Find the value of k that will make f continuous on. k = 28. Let Find the value of k that will make f continuous on. k = Subjective Short Answer 29. Evaluate the definite integral. Copyright Cengage Learning. Powered by Cognero. Page 8
30. Find the derivative of the function by using the rules of differentiation. 31. Find the indefinite integral. 32. Find the derivative of the function. 33. Find the derivative of the function. 34. Find the derivative of the function. 35. Find by solving the initial value problem. ; 36. Find by solving the initial value problem. ; 37. Use the laws of logarithms to simplify the expression. 38. Use the graph of the function f to find, and, if the limit exists. If it does not, answer none. Copyright Cengage Learning. Powered by Cognero. Page 9
= = = 39. Use the graph of the function f to find, and, if the limit exists. If it does not, answer none. Copyright Cengage Learning. Powered by Cognero. Page 10
= = = 40. Find for the function. Simplify your answer. 41. For the pair of supply and demand equations, where x represents the quantity demanded in thousands of units and p the unit price in dollars, find the equilibrium quantity and the equilibrium price. and x b = units p b = $ 42. Find an equation of the line that passes through the point and is parallel to the line 43. Find an equation of the line that passes through the points (2, 9) and ( 1, 12). Copyright Cengage Learning. Powered by Cognero. Page 11
Answer Key 1. a 2. a 3. d 4. d 5. c 6. c 7. a 8. d 9. e 10. d 11. c 12. a 13. b 14. b 15. b 16. b 17. a 18. b 19. b 20. e 21. e 22. a 23. 963 24. 8 25. 4 Copyright Cengage Learning. Powered by Cognero. Page 12
26. 2.26 27. -12 28. 2 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 4; 2; none 39. 2; 2; 2 40. 41. 3,000; 47 42. 43. Copyright Cengage Learning. Powered by Cognero. Page 13