(Test Bank) Applied Calculus for Business, Economics, and the Social and Life Sciences Expanded Edition

Laurence,Gerald,Dave,Michael, 11

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Test Bank for Applied Calculus for Business, Economics, and the Social and Life Sciences Expanded Edition, The downloadable file consists of 184 pages, and the total size of the file is 1.82 MB. Purchase now only for highly discounted price.

Author(s): Laurence, Gerald, Dave, Michael

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Page 1 Chapter 1 1. Compute the indicated value of the given function. 2( ) 2f x x x = − ; f (–1) Ans: 3 Difficulty: easy Section: 1.1 2. Compute the indicated value of the given function. 2( ) 3 2f x x = − ; f (–1) Ans: 1 Difficulty: easy Section: 1.1 3. Compute the indicated values of the given function. f ( x) = x – 3 + | x – 5| ; f (–4), f (–3), f (–2). A) 8, 8, 8 B) –2, –2, –2 C) –6, –4, –2 D) 2, 2, 2 Ans: D Difficulty: easy Section: 1.1 4. Compute the indicated value of the given function. f (x) = | x – 3 | + x – 5; f (2) A) –4 B) 2 C) –2 D) 1 Ans: C Difficulty: moderate Section: 1.1 5. Compute the indicated value of the given function. f (x) = | x + 2 | + 3| x – 1 |; f (–3) A) 13 B) –133 C) 9 D) 23 Ans: A Difficulty: moderate Section: 1.1 6. Compute the indicated value of the given function. 2–2 7 if 1( ) 8 if 1t tf t t t+ < −=+ ≥ −; f (–3) A) 13 B) 1 C) 17 D) –1 Ans: A Difficulty: easy Section: 1.1 7. Compute the indicated value of the given function. 21 if 1 ( ) 3 if 1 2 5 if 1x x f x x x x− < = =  − >; f (2) Ans: –8 Difficulty: moderate Section: 1.1 © 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.Chapter 1 Page 2 8. Compute the indicated value of the given function. 25 if 1 ( ) 4 if 1 7 2 if 1x x f x x x x− < = =  − >; f (2) Ans: 3 Difficulty: moderate Section: 1.1 9. Determine the domain of the given function. 29( )2xf xx−=+ A) all real numbers x B) all real numbers x except x = –2 C) all real numbers x except x = 3 and x = 7 D) all real numbers x except x = 3, x = –3, and x = –2 Ans: B Difficulty: easy Section: 1.1 10. Determine the domain of the given function. 4 3( ) 2 3 1f x x x x = + + + A) all real numbers x C) all real numbers x except x = –1 B) all real numbers x except x = 1 D) all real numbers x except x = 0 Ans: A Difficulty: easy Section: 1.1 11. Determine the domain of the given function. 4 3( ) 7 8 8f x x x x = + + + Ans: all real numbers x Difficulty: easy Section: 1.1 12. Determine the domain of the given function. ( ) 2 3f x x = − Ans: All real numbers x for which 3 2x≥ Difficulty: moderate Section: 1.1 13. Determine the domain of the given function. ( ) 3f x x = − A) all real numbers x C) all real numbers x for which 3x≥ B) all real numbers x except x = 3 D) all real numbers x for which 3 x≥ − Ans: C Difficulty: hard Section: 1.1 © 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.Chapter 1 Page 3 14. Determine the domain of the given function. 21( )3tf tt−=− Ans: All real numbers t for which t ≥ 1 or t ≤ –1 except t = 3 Difficulty: hard Section: 1.1 15. Determine the domain of the given function. 21( )2tf tt−=− Ans: All real numbers t for which t ≥ 1 or t ≤ –1 except t = 2 . Difficulty: hard Section: 1.1 16. Find the composite function ()( ) f g x . 3( ) 2f u u = + , g(x) = x + 3 A) f (g(x)) = 35x+ C) f (g(x)) =3 29 27 27x x x+ + + B) f (g(x)) =36x+ D) f (g(x)) =35 x x+ + Ans: C Difficulty: easy Section: 1.1 17. Find the composite function ()( ) f g x . 1( )f u uu= − , g(x) = 2 x – 3 Ans: f (g(x)) = 24 12 8 2 3x x x− + − − Difficulty: easy Section: 1.1 18. Find the composite function ()( ) f g x . 1( )f uu=, () 3 g x x = + A) f (g(x)) = 13x+ C) f (g(x)) = 31x+ B) f (g(x)) = 13xx+ + D) f (g(x)) = 1 3x+ Ans: D Difficulty: easy Section: 1.1 © 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.Chapter 1 Page 4 19. Find the difference quotient, ( )() f x h f x h+ −. ( )9f xx= A) ( )() f x h f x h+ − = 1 C) ( )() ( )9 f x h f x h x x h+ −= −+ B) ( )() f x h f x h+ − = 9 D) ( )() 9 f x h f x h x h+ −=+ Ans: C Difficulty: moderate Section: 1.1 20. Find the indicated composite function. f (x + 3) where 1( )f xx= A) f (x + 3) = 1 3x+ C) f (x + 3) = 13xx+ + B) f (x + 3) = 13x+ D) f (x + 3) = 31x+ Ans: A Difficulty: easy Section: 1.1 21. Find the indicated composite function. f (3x – 4) where 1( )f x xx= − Ans: f (3x – 4) = 2–9 24 15 3 4x x x+ − − Difficulty: easy Section: 1.1 22. Find functions h(x) and g (u) such that ( ) ( ) ( )f x g h x = : 7 2( ) 80 2 5f x x x = − − Ans: 2 7( ) 80 2 5 ; ( )h x x x g u u = − − = is one possible answer. Difficulty: easy Section: 1.1 23. Find functions h(x) and g (u) such that ( ) ( ) ( )f x g h x = : 5( ) 3 4 4f x x x= + + + Ans: 5( ) 4; ( ) 3h x x g u u u= + = + is one possible answer. Difficulty: easy Section: 1.1 © 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.Chapter 1 Page 5 24. An efficiency study of the morning shift at a certain factory indicates that an average wo rker who arrives on the job at 8:00 A.M. will have assembled 3 2( ) 5 16f x x x x = − + + transistor radios x hours later. How many radios will such a worker assemble between 10:00 and 11:00 A.M.? A) 20 B) 22 C) 15 D) 18 Ans: B Difficulty: moderate Section: 1.1 25. To study the rate at which animals learn, a psychology student performed an experiment in which a rat was sent repeatedly through a laboratory maze. Suppose the time required for the rat to traverse the maze on the nth trial was approximately 22 4( ) 5T nn n= + − minutes. How many minutes does it take the rat to traverse the maze on the 2nd trial? Ans: T(2) = 5 min Difficulty: hard Section: 1.1 26. To study the rate at which animals learn, a psychology student performed an experiment in which a rat was sent repeatedly through a laboratory maze. Suppose the time required for the rat to traverse the maze on the thn trial was approximately 28 16( ) 4T nn n= + − minutes. How long does it take the rat to traverse the maze in the second trial? Ans: T(2) = 4 minutes Difficulty: hard Section: 1.1 27. A ball is thrown upward in such a way that t seconds later, it is ()216 64 80 H t t t = − + + feet above the ground. How many seconds later does the ball hit the ground? Ans: H(t) = 0 at t = 5 seconds Difficulty: hard Section: 1.1 28. A ball is thrown upward in such a way that t seconds later it is ()2–15 60 75 H t t t = + + feet above the ground. When does the ball hit the ground? Ans: H(t) = 0 at t = 5 seconds. Difficulty: hard Section: 1.1 29. At a certain factory, the total cost of manufacturing q units during the daily production run is 2( ) 2 297C q q q = + + dollars. On a typical workday, q(t) = 17t units are manufactured during the first t hours of a production run. How many dollars are spent during the first 3 hours of production? Ans: $3,000 Difficulty: hard Section: 1.1 © 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.Chapter 1 Page 6 30. At a certain factory, the total cost of manufacturing units during the daily production run i s 2( ) 2 260C q q q = + + dollars. On a typical day, q(t) = 15t units are manufactured during the first hours of a production run. How much is spent during the first 3 hours of production? Ans: $2,375 Difficulty: hard Section: 1.1 © 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.Chapter 1 Page 7 31. Plot the given point in a rectangular coordinate system. (–4, 1) A) (-4, 1)xy (E ach gridline represents one unit.) B) (-4, 1)xy (E ach gridline represents one unit.) C) (-4, 1)xy (E ach gridline represents one unit.) D) (-4, 1) xy © 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.Chapter 1 Page 8 (E ach gridline represents one unit.) Ans: B Difficulty: easy Section: 1.2 32. Find the distance between the given points. (4, 8) and (–8, 7) A) 13 D= B) D = 13 C) D = 145 D) 145 D= Ans: D Difficulty: easy Section: 1.2 33. Sketch the graph of the given function. 2( ) 2f x x = + ( T ick marks are spaced one unit apart. ) A) Graph a B) Graph b C) Graph c D) Graph d Ans: D Difficulty: moderate Section: 1.2 34. Find the points of intersection (if any) of the given pair of curves. y = 3x – 1 and y = 3 – 5 x Ans: 1 1,2 2     Difficulty: easy Section: 1.2 35. Find the points of intersection (if any) of the given pair of curves. y = x + 8 and y = 2x + 4 A) (4, 12) B) (1, –4) C) (0, 6) D) (12, 20) Ans: A Difficulty: moderate Section: 1.2 © 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.Chapter 1 Page 9 36. Find the points of intersection (if any) of the given pair of curves. y = 6x – 1 and y = 2x – 8 Ans: 7 23– , –4 2     Difficulty: easy Section: 1.2 37. Find the points of intersection (if any) of the given pair of curves. y = x + 3 and y = 2x + 4 A) (1, –4) B) (–1, 2) C) (0, 3) and (1, 4) D) (1, 6) Ans: B Difficulty: moderate Section: 1.2 38. Find the points of intersection (if any) of the given pair of curves. 2y x= and y = 3x – 2. A) (0,0) B) There are no points of intersection. C) (2, 4) D) (1, 1), (2, 4) Ans: D Difficulty: moderate Section: 1.2 39. If an object is thrown vertically upward with an initial speed of 128 ft/sec, its height (in feet) t seconds later is given by 2( ) 16 128H t t t = − + . Graph the function H(t) and use t he graph to determine when the object will hit the ground. Ans: 8 seconds Difficulty: hard Section: 1.2 40. A ball is thrown upward in such a way that t seconds later, it is 216 96 144 s t t= − + + f eet above the ground. Sketch the graph of s(t) and determine the maximum height in feet a ttained by the ball. Ans: 288 ft Difficulty: hard Section: 1.2 © 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.Chapter 1 Page 10 41. Find the slope (if possible) of the line that passes through the given pair of points. (–1, 5) and (7, 2) Ans: 3 8− Difficulty: easy Section: 1.3 42. Find the slope (if possible) of the line that passes through the given pair of points. (5, 0) and (3, 4) A) –2 B) 2 C) 1 2− D) 1 2 Ans: A Difficulty: easy Section: 1.3 43. Find the slope (if possible) of the line that passes through the given pair of points. (12, 0) and (16, 17) A) 17 4 B) 4 17 C) 4 17− D) 17 4− Ans: A Difficulty: easy Section: 1.3 44. Find the slope (if possible) of the line that passes through the given pair of points. (0, 5) and (8, 7). A) 4 B) 1 4 C) 0 D) The slope is undefined. Ans: B Difficulty: easy Section: 1.3 45. Find the slope (if possible) of the line that passes through the given pair of points. (6, 4) and (9, –4). Ans: 8 3− Difficulty: easy Section: 1.3 46. Find the slope of the line passing through (6, –9) and (2, 8). Round your answer to two decimal places, if necessary. A) –4.25 B) –0.24 C) 0.24 D) 4.25 Ans: A Difficulty: easy Section: 1.3 47. Find the slope and y-intercept of the line whose equation is given. 5 y = 8x A) slope 8, y -intercept 0 C ) slope 8 5 , y-intercept 0 B) slope 8, y -intercept 5 D) slope 8 5− , y-intercept 0 Ans: C Difficulty: moderate Section: 1.3 © 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.Chapter 1 Page 11 48. Find the slope and y-intercept (if they exist) of the line 7 y = 2x. A) Slope is 2 7 and y -intercept is 0. C) Slope is 2 and y-intercept is 0. B) Slope is 2 and y-intercept is 7. D) Slope is 7 2 and y -intercept is 0. Ans: A Difficulty: easy Section: 1.3 49. Find the slope and y-intercept of the line whose equation is given. y = 2x – 5. A) slope 2, y -intercept –5 C ) slope 1 2 , y-intercept –5 B) slope 2, y -intercept 5 D) slope 1 2 , y-intercept 5 Ans: A Difficulty: easy Section: 1.3 50. Find the slope of the line whose equation is given. 3 x + 5y = –7 Ans: 3 5− Difficulty: moderate Section: 1.3 51. Find the slope of the line whose equation is given. 3 x – 5y = 9. Ans: 3 5 Difficulty: moderate Section: 1.3 52. What is the slope of the line 6 x + 9y = –7? Round your answer to two decimal places, if n ecessary. A) –1.5 B) 1.5 C) 0.67 D) –0.67 Ans: D Difficulty: easy Section: 1.3 53. Find the slope of the line with the following equation 2 x + 3y = –5. Ans: Slope: 2 3− Difficulty: moderate Section: 1.3 54. Find the slope and y-intercept of the line 7 y – 6x = 6. Ans: Slope: 6 7; y-intercept: 6 7 Difficulty: moderate Section: 1.3 © 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.Chapter 1 Page 12 55. Find the slope and y-intercept of the line whose equation is given. 13 5x y+ = Ans: Slope: 5 3−; y-intercept: 5 Difficulty: hard Section: 1.3 56. Find the slope and y-intercept of the line whose equation is given. 12 3x y+ = A) Slope: 3 2−; y-intercept: 3 C) Slope: 1 2; y-intercept: 1 B) Slope: 3 2; y-intercept: 1 D) Slope: 3 2; y-intercept: 1 2 Ans: A Difficulty: moderate Section: 1.3 57. Write an equation for the line through (3, 0) with slope 2. A) y = 2x – 6 B) y = 2x – 3 C) y = 2x + 6 D) y = 2x + 3 Ans: A Difficulty: moderate Section: 1.3 58. Write an equation for the line with the given properties. Through (3, –1) with slope 2 Ans: y = 2x – 7 Difficulty: moderate Section: 1.3 59. Write an equation for the line through (5, 4) and parallel to the x-axis. A) x = 5 B) x = –5 C) y = 4 D) y = –4 Ans: C Difficulty: easy Section: 1.3 60. Find an equation of the line parallel to the line y-axis and through the point (3, 7). Ans: x = 3. Difficulty: moderate Section: 1.3 61. What is the equation of the line through the points (7, –1) and (1, 15)? Round numbers to two decimal places, if necessary. A) y = –0.38 x + 17.67 C ) y = –2.67 x + 0.06 B) y = –0.38 x + 0.06 D) y = –2.67 x + 17.67 Ans: D Difficulty: easy Section: 1.3 © 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.Chapter 1 Page 13 62. Between August 29 and September 4, 2005, the price of gasoline increased steadily due t o the impact of hurricane Katrina. The average price per gallon in Cincinnati on August 29 was $2.60, and on September 4 if was $3.10. Write a linear function C(x) that d escribes the cost per gallon of gas in Cincinnati in terms of days after August 29. Round the slope to three decimal places, if necessary. Use your function to find how much gas would have cost on October 1 if the price had continued to increase at that rate. Ans: C(x) = 0.083 x + 2.60; $5.34 Difficulty: moderate Section: 1.3 63. The cost of renting a backhoe at one distributor is $325, plus $35 per day. Write a linear function C(x) that describes the cost of renting the backhoe for x days, then use your f unction to find how much it would cost to rent it for 6 days. A) ( ) 325 35; $1,985C x x = + C) ( ) 325 35 ; $535C x x = + B) ( ) ( ) 6 325 35 ; $3, 210C x x = + D) ( ) 35 319; $529C x x = + Ans: C Difficulty: easy Section: 1.3 64. Each unit of a certain commodity costs p = 23x + 24 cents when x units of the commodity a re produced. If all units are sold at this price, express the revenue derived from the sales as a function of x. A) x(23x + 24) cents C ) 223 24x+ cents B) 22 x + 24 cents D) 24 x + 24 cents Ans: A Difficulty: hard Section: 1.4 65. A manufacturer's total cost consists of a fixed overhead of $250 plus production costs of $70 per unit. Express the total cost in dollars as a function of the number of units produced. Ans: C(x) = 70 x + 250 Difficulty: hard Section: 1.4 66. A manufacturer's total cost consists of a fixed overhead of $100 plus production costs of $40 per unit. Express the total cost in dollars as a function of the number of units produced. Ans: C(x) = 40 x + 100. Difficulty: hard Section: 1.4 67. A farmer is planning to plant a rectangular garden with an area of 4,000 square yards. The garden is to be fenced on all four sides. Express the number of yards of fencing required as a function of x, the long side of the fence. Ans: 4,0002 2s xx = +   Difficulty: hard Section: 1.4 © 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.Chapter 1 Page 14 68. A farmer is planning to plant a rectangular garden with an area of 6,400 square yards. T he garden is to be fenced on all four sides. Express the number of yards of fencing required as a function of x, the long side of the fence. Ans: 12,8002xx+ Difficulty: hard Section: 1.4 69. A rectangle is constructed inside a circle of radius r with the corners of the rectangle lying on the circle. Express the area A of the rectangle as a function of the radius r if the width of one side of the rectangle is 2. Ans: 24 1A r= − Difficulty: moderate Section: 1.4 70. A closed cylindrical can has a surface area of 360 π square inches. Express the volume of the can as a function of its radius, r. A) 2( ) (180 )π V r r r = − cubic inches C) 2( ) 360π V r r = cubic inches B) V(r) = 180 πr cubic inches D) 3( ) (180 )π V r r = − cubic inches Ans: A Difficulty: hard Section: 1.4 71. A cylindrical can is to have a volume of 36 π cubic inches. The cost of the material used for the top and bottom of the can is 4 cents per square inch, and the cost of the material used for the curved side is 3 cents per square inch. Express the cost in cents of constructing the can as a function of its radius. Ans: 22168ππ C rr= + Difficulty: hard Section: 1.4 72. A cylindrical can is to have a volume of 27 π cubic inches. The cost of the material used for the top and bottom of the can is 4 cents per square inch, and the cost of the material used for the curved side is 5 cents per square inch. Express the cost of constructing the can as a function of its radius. Ans: 28 270ππrr+ cents Difficulty: hard Section: 1.4 © 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.Chapter 1 Page 15 73. A closed box with a square base is to have a volume of 40 cubic meters. The material for t he top and bottom of the box costs $2 per square meter, and the material for the sides costs $1 per square meter. Express the construction cost of the box as a function of the length of its base, x. A) 2( ) 160 2C x x x = + + dollars C) 240( ) 2C x xx= + dollars B) 22( ) 2 4C x xx= + + dollars D) 2160( ) 4C x xx= + dollars Ans: D Difficulty: hard Section: 1.4 74. The supply and demand functions, S(x) and D(x), respectively, for a certain commodity are given in terms of the level of production x. S( x) = 2 x + 30, D(x) = 360 – x. Find the value of x e f or which equilibrium occurs. Ans: 110 Difficulty: easy Section: 1.4 75. Two car rental agencies are competing. One agency rents cars for 35 dollars per day and 35 cents a mile; the other agency rents cars for 20 dollars per day and 40 cents a mile. For a 3 day trip, how many miles must you travel to have the total cost be the same with each agency? Round to the nearest whole mile , if necessary. A) 900 miles B) 300 miles C) 43 miles D) 38 miles Ans: A Difficulty: hard Section: 1.4 76. Two jets bound for San Diego leave Boston 20 minutes apart. The first travels at 450 miles per hour, while the second goes 500 miles per hour. How how many hours after the second plane departs will the second plane pass the first? Ans: 3 hours after the second plane leaves Difficulty: hard Section: 1.4 77. Two jets bound for San Diego leave Boston 20 minutes apart. The first plane travels at 240 miles per hour, while the second plane goes 280 miles per hour. At what time will the second plane pass the first? Ans: 2 hours after the second plane departs. Difficulty: hard Section: 1.4 78. An appliance manufacturer can sell refrigerators for $1,500 apiece. The manufacturer's total cost consists of a fixed overhead of $30,000 plus production cost of $1,000 per refrigerator. How many refrigerators must be sold for the manufacturer to break even? Ans: 60 Difficulty: hard Section: 1.4 © 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.Chapter 1 Page 16 79. An appliance manufacturer can sell refrigerators for $600 apiece. The manufacturer's t otal cost consists of a fixed overhead of $12,000 plus production cost of $400 per refrigerator. How many refrigerators must be sold for the manufacturer to break even? Ans: 60 Difficulty: hard Section: 1.4 80. A company makes a certain product for $4 each and sells it for $8. If the company has overhead expenses of $10,000 per year, how many of its products must be made and sold to break even? A) 10,000 B) 20,000 C) 40,000 D) 2,500 Ans: D Difficulty: hard Section: 1.4 81. If f (x) is graphed below, find 1lim ( ) xf x → if it exists. Ans: 2 Difficulty: moderate Section: 1.5 © 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.Chapter 1 Page 17 82. If f (x) is graphed below, find 1lim ( ) xf x → if it exists. Ans: 1 Difficulty: moderate Section: 1.5 83. Find the indicated limit if it exists. 2 1lim (2 3 1) xx x →− + Ans: 0 Difficulty: easy Section: 1.5 84. Find the indicated limit if it exists. ( )2 1lim 6 4 1 xx x →− + Ans: 3 Difficulty: easy Section: 1.5 85. Find the indicated limit if it exists. ( ) 3lim 4 xx →+ A) 7 B) 3 C) Does not exist D) –1 Ans: A Difficulty: easy Section: 1.5 86. Find the indicated limit if it exists. 12 1lim3xx x→− + Ans: 1 4 Difficulty: easy Section: 1.5 © 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.Chapter 1 Page 18 87. Find the indicated limit if it exists. 222lim4xx x→− − Ans: 1 4 Difficulty: moderate Section: 1.5 88. Find the indicated limit if it exists. 2 13 5 2lim2 1xx x x→− + + Ans: 0 Difficulty: easy Section: 1.5 89. Find the indicated limit if it exists. 13 1lim7xx x→− + Ans: 1 4 Difficulty: easy Section: 1.5 90. Find the indicated limit if it exists. 222lim4xx x→− − Ans: 1 4 Difficulty: moderate Section: 1.5 91. Find the indicated limit if it exists. 2 213 2lim1xx x x→+ + − A) 3 2 B) 3 C) 6 D) Does not exist Ans: D Difficulty: moderate Section: 1.5 92. Find the indicated limit if it exists. 42lim4xx x→− − A) Does not exist B) 4 C) 1 4− D) 1 4 Ans: D Difficulty: hard Section: 1.5 © 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.Chapter 1 Page 19 93. Find () lim xf x →+∞ and () lim xf x →−∞. If the limiting value is infinite indicate whether it is +∞ or – ∞. f (x) = (5 – 2 x)(x – 1) A) – ∞, 0 B) + ∞, 0 C) – ∞, –∞ D) + ∞, +∞ Ans: C Difficulty: moderate Section: 1.5 94. Find () lim xf x →+∞ and () lim xf x →−∞. If the limiting value is infinite indicate whether it is +∞ or – ∞. ( )3 32 9 6 + – 3xf xx x−= A) 3 2−, 3 2 B) 3 2−, 3 2− C) +∞, –∞ D) – ∞, +∞ Ans: B Difficulty: moderate Section: 1.5 95. Complete the table by evaluating f (x) at the specified values of x. Then use the table to estimate the indicated limit, or show that it does not exist. 2 4( ) 3 13 ; lim ( ) xf x x x f x →= − 3.9 3.99 3.999 4 4.001 4.01 4.1 ( )x f x Ans: 3.9 3.99 3.999 4 4.001 4.01 4.1 ( ) –5.07 –4.1097 –4.010997x f x 4–3.988997 –3.8897 –2.87 lim ( ) –4 xf x →= Difficulty: easy Section: 1.5 96. Complete the table by evaluating f (x) at the specified values of x. Then use the table to estimate the indicated limit, or show that it does not exist. 2 43 48( ) ; lim ( )4xxf x f xx→−−=+ 4.1 4.01 4.001 4 3.999 3.99 3.9 ( )x f x− − − − − − − Ans: 4.1 4.01 4.001 4 3.999 3.99 3.9 ( ) 24.3 24.03 24.003x f x− − − − − − − − − − 423.997 23.97 23.7 lim ( ) 24 xf x →−− − − = − Difficulty: easy Section: 1.5 © 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.Chapter 1 Page 20 97. Complete the table by evaluating f (x) at the specified values of x. Then use the table to estimate the indicated limit, or show that it does not exist. 65 7( ) ; lim ( )6xxf x f xx→+=− 5.9 5.99 5.999 6 6.001 6.01 6.1 ( )x f x Ans: 5.9 5.99 5.999 6 6.001 6.01 6.1 ( ) –365 –3,695 –36,995x f x 637,005 3,705 375 l im ( ) does not exist xf x → Difficulty: easy Section: 1.5 98. An efficiency consultant determines that when new workers are hired to wait tables at an upscale restaurant, the average number of tables they can wait on in a 6 hour shift is given by ( )25.3 50 14 0.1 0.8x xN xx+ +=+ where x is the number of shifts they've worked since being hired. What happens to an average waiter's productivity in the long run (as x→ ∞ )? A) It approaches 14 tables per shift. C) It approaches 53 tables per shift. B) It approaches 23 tables per shift. D) It increases without bound. Ans: B Difficulty: moderate Section: 1.5 99. As a rumor spreads across a college campus, the number of people that have heard it can be modeled by the equation ( )2 26,000 2,700 ( 3)t tN tt+=+ where t is days since the rumor started spreading. What happens to the number of people that have heard the rumor in the long run (as t→ ∞ )? Ans: It approaches 6,000. Difficulty: easy Section: 1.5 100. Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is +∞ or –∞. 42lim4 xx x−→− − A) 2 B) –2 C) 1 4 D) 1 4− Ans: C Difficulty: hard Section: 1.6 © 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.Chapter 1 Page 21 101. Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is +∞ or –∞. 366lim36 xx x−→− − Ans: 1 12 Difficulty: hard Section: 1.6 102. Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is +∞ or –∞. 366lim36 xx x−→− − Ans: 1 12 Difficulty: hard Section: 1.6 103. Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is +∞ or –∞. 11lim1 xx x+→− − Ans: +∞ Difficulty: hard Section: 1.6 104. Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is +∞ or –∞. 55lim5 xx x+→− − Ans: + ∞ Difficulty: hard Section: 1.6 105. Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is +∞ or –∞. 2lim ( ) xf x −→ where 2if 2( ) 1 if 2x xf x x x ≤=+ > Ans: 4 Difficulty: hard Section: 1.6 © 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.Chapter 1 Page 22 106. Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is +∞ or –∞. 2lim ( ) xf x +→ where 2if 2( ) 1 if 2x xf x x x ≤=+ > Ans: 3 Difficulty: hard Section: 1.6 107. Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is +∞ or –∞. 2lim ( ) xf x −→ where 25 if 2( ) if 2x xf x x x+ <=≥  A) 7 B) 0 C) 4 D) There is none Ans: A Difficulty: hard Section: 1.6 108. True or False: 3lim ( ) 3 xf x −→= where if 3( )1 if 3x xf xx x< =+ ≥ A) True B) False Ans: A Difficulty: hard Section: 1.6 109. Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is +∞ or – ∞. 1lim ( ) xf x −→ where 2if 1( ) 3 if 1x xf x x x ≤=+ > Ans: 1 Difficulty: hard Section: 1.6 110. List all values of x for which f (x) is not continuous. 14 21( )7xf xx−=− Ans: 7 Difficulty: moderate Section: 1.6 111. List all values of x for which f (x) is not continuous. 5 10( )2xf xx−=− Ans: 2 Difficulty: moderate Section: 1.6 © 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.Chapter 1 Page 23 112. List all values of x for which f (x) is not continuous. 25 1( )xf xx+= Ans: 0 Difficulty: moderate Section: 1.6 113. List all values of x for which f (x) is not continuous. 22 1( )xf xx x+=+ . A) –1 B) 0 and –1 C) 1 2− D) None Ans: B Difficulty: moderate Section: 1.6 114. List all values of x for which f (x) is not continuous. 27 1( )xf xx+= Ans: 0 Difficulty: moderate Section: 1.6 115. Find all values of x for which the given function is not continuous. 2 23 2( )4 3x xf xx x+ +=+ + Ans: –1 and –3 Difficulty: hard Section: 1.6 116. Decide if the given function is continuous at the specified value of x. 4 if 1( ) ; 14 1 if 1x xf x xx x+ <= = + ≥ A) No, the function is not continuous at x = 1. B) Yes, the function is continuous at x = 1. Ans: B Difficulty: easy Section: 1.6 117. List all the values of x for which the given function is not continuous. 4if 3( ) 81 if 3x xf x x ≤=> A) x = 0 B) x = 3 C) x = ±3 D) The function is continuous for all values of x. Ans: D Difficulty: easy Section: 1.6 © 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.Chapter 1 Page 24 118. Find all the values of x for which the given function is not continuous. 24 if 5( ) 4 if 5x xf x x+ ≤=>  Ans: 5 Difficulty: moderate Section: 1.6 119. Find all the values of x for which the given function is not continuous. 25 if 3( ) 3 if 3x xf x x+ ≤=>  Ans: 3 Difficulty: moderate Section: 1.6 © 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. Page 25 Chapter 2 1. The equation of the line tangent to the graph of 2( ) 3f x x x = + at x = 2 is A) y = 7x – 4 B) y = 7x – 422 C) y = 7x – 2 D) y = 7x – 144 Ans: A Difficulty: moderate Section: 2.1 2. The equation of the line tangent to the graph of 2( ) 4f x x x = + at x = 3 is A) y = 10 x – 9 B) y = 10 x – 108 C) y = 10 x – 3 D) y = 10 x – 27 Ans: A Difficulty: moderate Section: 2.1 3. The equation of the line tangent to the graph of ( ) 3f x x = at x = 1 is A) 1 1 2 2y x= − B) 1 1 2 2y x= + C) 3 3 2 2y x= + D) 312y x= − Ans: C Difficulty: moderate Section: 2.1 4. For f (x) = 5 – x2, find the slope of the secant line connecting the points whose x- coordinates are x = –6 and x = –5.9. Then use calculus to find the slope of the line that is tangent to the graph of f at x = –6. Ans: Slope of secant line: 11.9; Slope of tangent line: 12 Difficulty: moderate Section: 2.1 5. For 3( )f x x= − , find the average rate of change of f (x) with respect to x as x changes from 144 to 145. Then use calculus to find the instantaneous rate of change at x = 144. Round your answer to six decimal places, if necessary. A) Average rate of change: 0.000864; Instantaneous rate of change: –0.125 B) Average rate of change: –0.000864; Instantaneous rate of change: 0.000868 C) Average rate of change: –0.000864; Instantaneous rate of change: 0.125 D) Average rate of change: 0.000864; Instantaneous rate of change: 0.000868 Ans: D Difficulty: hard Section: 2.1 6. If f (x) represents the price per barrel of oil in terms of time, what does 0 0 ( ) ( )f x h f x h+ − represent? What about 0 0 0( ) ( )lim hf x h f x h→+ −? Ans: The average rate of change of oil price with respect to time on the time interval [ x0, x0 + h] ; the instantaneous rate of change of oil price with respect to time at time x0. Difficulty: easy Section: 2.1 7. True or False: Differentiating 3( ) 3 1f x x x = − + gives 23x. A) True B) False Ans: B Difficulty: easy Section: 2.2 © 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.