Final Review 210+Fa13 - Arizona State Universitydiane/Spring_2014/MAT_210/Final_Review... ·...

Final_Review_210_Fa13

Multiple Choice Identify the choice that best completes the statement or answers the question.

____ 1. Estimate the limit numerically.

a. -2 b. c. d. e.


a. b. c. d. e.


a. b. c.

d.

e.


a.

b. c. d. e.


a. b. c. d. e.


a. b. c. d. e.

____ 7. Use the graph to compute

a.

b.

c.

d. e. does not exist

____ 8. Use the graph to compute

a.

b.

c.

d.

e. does not exist

____ 9. The graph of a function is given. Determine whether is continuous on its domain.

a. Discontinuous b. Continuous

____ 10. The graph of a function is given. Determine whether is continuous on its domain.

a. Continuous b. Discontinuous

____ 11. Use a graph of f or some other method to determine what, if any, value to assign to f(a) to make f continuous at x = a.

a. b. c. d. e. No value of will make it continuous at .

____ 12. Determine what, if any, value to assign to f(a) to make f continuous at x = a.

;

a. b. c. d. e. No value of f(0) will make it continuous at 0.

____ 13. Use a graph to determine whether the function is continuous on its domain. If it is not continuous on its domain, list the points of discontinuity.

a. The point of discontinuity: 2. b. The function is continuous on its domain. c. The points of discontinuity: -2, 0. d. The point of discontinuity: 0. e. The points of discontinuity: 2, 0.

____ 14. Calculate the limit algebraically.

a. 8 b. –2 c. 0 d. 6 e. 10

____ 15. Calculate the limit algebraically.

a. b. c. d. e. 0

____ 16. Find all points of discontinuity of the function.

a. , b. c. , , d. e. The function is continuous everywhere.

____ 17. Calculate the average rate of change of the given function over the interval .

p($) 2 2.25 2.5 q(p) (items) 600 400 250 a. 4,000 b. 800 c. –50 d. –200 e. –800

____ 18. Calculate the average rate of change of the given function (Inflation (%) of Budget deficit (% of GNP)) over the interval .

a. 1 b. –0.5 c. 8 d. 5 e. –20

____ 19. Calculate the average rate of change of the given function over the interval .

a. 4 b. –44 c. 40 d. –4 e. –40

____ 20. At which labeled point is the slope of the tangent is greatest?

a. P b. Q c. R

____ 21. At which labeled point is the slope of the tangent least (in the sense that -7 is less than 1)?

a. Q b. P c. R

____ 22. At which labeled point is the slope of the tangent greatest?

a. Q b. P c. R

____ 23. Find an equation of the tangent line to the graph of the function at the point that has

x-coordinate .

a. b. c. d. e.

____ 24. On January 1, 1996, America Online was the largest on-line service provider, with 4 million subscribers, and it was adding new subscribers at a rate of 48,000 per week. If is the number of America Online subscribers t weeks after January 1, 1996, what do the given data tell you about values of the function and its derivative?

a. A(0) = 0.048, A'(0) = 4 b. A(0) = 4.5, A'(0) = 0.047 c. A(0) = 8, A'(0) = 0.048 d. A(0) = 3.5, A'(0) = 0.048 e. A(0) = 4, A'(0) = 0.048

____ 25. Find the derivative of the function.

a.

b.

c.

d.

e.

____ 26. If a stone is dropped from a height of 300 feet, its height s after t seconds is given by with s in feet. a. Find the stone's velocity at seconds. b. When does it reach the ground, and how fast is it travelling when it hits the ground? Round your answers to the nearest hundredth. a. -200, 3.87, -154.92 b. 200, 3.87, -154.92 c. -200, 15.00, -600.00 d. -100, 1.94, -77.46 e. -10, 3.87, -600.00

____ 27. For the cost function, find the marginal cost at the given production level x.

a. $4.80 per item b. $5.00 per item c. $4.81 per item d. $5.20 per item e. $4.78 per item

____ 28. Find the value of x for which the marginal profit is zero.

a. x = 2,500 b. x = 10,000 c. x = –5,000 d. x = 5,000 e. x = 7,000

____ 29. Your monthly profit (in dollars) from selling magazines is given by where x is the number of magazines you sell in a month. If you are currently selling x = 100 magazines per month, find your profit and your marginal profit.

a. P(100) = $430, P'(100) = $4.15 b. P(100) = $417.32, P'(100) = $0.35 c. P(100) = $860, P'(100) = $4.65 d. P(100) = $417.32, P'(100) = $4.15 e. P(100) = $215, P'(100) = $2.08

____ 30. Calculate . You need not expand your answer.

a.

b.

c.

d.

e.

____ 31. Calculate .

a.

b.

c.

d.

e.


a.

b.

c.

d.

e.


a.

b.

c.

d.

e.

____ 34. Find the equation of the line tangent to the graph of the given function at the point .

a.

b. c. d. e.

____ 35. A mold culture in a dorm refrigerator is circular and growing. The radius is increasing at a rate of 0.4 cm/day. How fast is the area growing when the culture is 3 centimeters in radius? (The area of a disc of radius r is

.)

a.

b.

c.

d.

e.

____ 36. Find the derivative of the following function.

a.

b.

c.

d.

e. none of these

____ 37. Find the derivative of the following function.

a.

b.

c.

d.

e. none of these

____ 38. Find the derivative of the function.

a.

b.

c.

d.

e. none of these

____ 39. If $21,000 is invested in a savings account yielding 5.5% per year, compounded semiannually, how fast is the balance growing after 3 years?

a. $938.57 per year b. $1,340.81 per year c. $1,676.02 per year d. $1,877.14 per year e. $2,413.47 per year

____ 40. Find using implicit differentiation.

a.

b.

c.

d.

e.


a. b.

c.

d.

e.


a.

b.

c.

d.

e.

____ 43. Find the equation of the tangent line for at the point .

a.

b. c. d.

e.

____ 44. Find the exact location of all the relative and absolute extrema of the function with domain .

a. - absolute minimum

b. - absolute minimum

c. - relative maximum

d. - relative maximum e.

- absolute maximum

____ 45. Find the exact location of all the relative and absolute extrema of the function with domain .

a. (0, 1) - absolute maximum b. (0, 8) - relative minimum c. (1, 0) - absolute maximum d. (1, 5) - absolute maximum e. (0, 1) - absolute minimum

____ 46. Maximize with .

a. P = 216 b. P = 1,200 c. P = 4 d. P = 108 e. P = 72

____ 47. Minimize with

a. F = 68 b. F = 256 c. F = 204 d. F = 4 e. F = 272

____ 48. For a rectangle with area 81 to have the smallest perimeter, what dimensions should it have?

a. b. c. d. e.

____ 49. I want to fence in a rectangular vegetable patch. The fencing for the east and west sides costs $5 per foot, while the fencing for the north and south sides costs only $3 per foot. I have a budget of $150 for the project. What is the largest area I can enclose?

a. 375 square feet b. 15 square feet

c. 187.5 square feet d. 93.75 square feet e. 150 square feet


a. b. c. d. e.


a. b. c.

d.

e.


a. b.

c.

d.

e.

____ 53. The position s of a point (in feet) is given as a function of time (in seconds).

a. Find its acceleration as a function of . b. Find its acceleration at the specified time. a. a(t) = 24 ft/sec2, a(t = 2) = -24 ft/sec2

b. a(t) = 5 ft/sec2, a(t = 2) = 5 ft/sec2

c. a(t) = 20 ft/sec2, a(t = 2) = 20 ft/sec2

d. a(t) = -2 ft/sec2, a(t = 2) = 2 ft/sec2

e. a(t) = -20 ft/sec2, a(t = 2) = -20 ft/sec2

____ 54. The graph of a function is given.

Find the coordinates of all points of inflection of this function (if any). a. b. c. d. e.

____ 55. Find the coordinates of all relative and absolute extrema.

a. (0, 0) b. (0, 0), (3, 4.5) c. (–3, –4.5), (3, 4.5) d. (–3, –4.5), (3, 4.5), (0, 0) e. (–1, 1), (0, 0)

____ 56. Sketch the graph of the function, labeling all relative and absolute extrema and points of inflection, and vertical and horizontal asymptotes. Check your graph using technology.

a.

b.

c.

d.

e.

____ 57. Combined SAT scores in the United States could be approximated by

in the years 1968 - 1988. Here t is the number of years since 1968, and T is the combined SAT score average for the United States. Find all points of inflection of the graph of T, and interpret the result. a. (0, 0) b. (15.85, 903.33), (21.58, 904.30) c. (18.71, 903.81) d. (0, 0), (20, 904.12) e. (20, 904.12)

____ 58. There are presently N = 200 cases of Bangkok flu, and the number is growing by 50 new cases every month. Rewrite the rate in mathematical notation.

a.

b. c. d.

e.

____ 59. The area of a circular sun spot is growing at a rate of 1,200 km 2/s. How fast is the radius growing at the instant when it equals 10,000 km?

a. 0.060 km/s b. 0.038 km/s c. 0.019 km/s d. 8.333 km/s e. 0.000 km/s

____ 60. A rather flimsy spherical balloon is designed to pop at the instant its radius has reached 5 cm. Assuming the balloon is filled with helium at a rate of 5 cm 3/s, calculate how fast the diameter is growing at the instant it pops.

The volume of a sphere of radius r is .

a. 0.016 cm/s b. 0.127 cm/s c. 0.159 cm/s d. 0.212 cm/s e. 0.032 cm/s

____ 61. Demand for your tie-dyed T-shirts is given by the formula

where p is the price in dollars you can charge to sell q T-shirts per month. If you currently sell T-shirts for $10 each and you raise price by $2 each month, how fast will the demand drop? a. 10 T-shirts per month b. 400 T-shirts per month c. 40 T-shirts per month d. 20,000 T-shirts per month e. 80 T-shirts per month

____ 62. A right conical circular vessel is being filled with green industrial waste at a rate of 150 cubic meters per second. How fast is the level rising after 150 cubic meters have been poured in? (The cone has height 75 m and radius 45 m at its brim. The volume of a cone of height h and cross-sectional radius r at its brim is given

by .)

a. 3.4 m/s b. 1.1 m/s c. 0.2 m/s d. 3.6 m/s e. 0.7 m/s

____ 63. The weekly sales in Honolulu Red Oranges is given by the following equation.

Calculate the elasticity of demand for a price of $23 per orange. a. 0.63 b. -0.63 c. -1.35 d. –0.09 e. 1.35

____ 64. The consumer demand curve for tissues is given by

where p is the price per case of tissues and q is the demand in weekly sales. At what price should tissues be sold to maximize the revenue? a. $72.00 b. $108.00 c. $36.00 d. $32.00 e. $54.00

____ 65. The consumer demand curve for Professor Stefan Schwartzenegger dumbbells is given by

where p is the price per dumbbell and q is the demand in weekly sales. Find the price Professor Schwartzenegger should charge for his dumbbells in order to maximize revenue. a. $29 b. $34 c. $38 d. $342 e. $40

____ 66. Evaluate the integral.

a.

b.

c.

d.

e.


a.

b.

c.

d.

e.


a.

b.

c.

d.

e.

____ 69. Find if and the tangent line at has slope .

a.

b.

c.

d.

e.

____ 70. The marginal cost of producing the box of computer disks is and the fixed cost is $150,000.

Find the cost function

a.

b.

c.

d.

e.

____ 71. The velocity of a particle moving in a straight line is given by . Find an expression for the positionafter a time . a. b. c.

d.

e.


a.

b.

c.

d.

e.


a.

b.

c.

d.

e.


a.

b.

c.

d.

e.


a.

b.

c.

d.

e.


a.

b. c.

d.

e.

____ 77. Find if and the tangent line at ( x, f(x)) has the slope.

a.

b.

c.

d.

e.

____ 78. The marginal cost of producing the xth roll of film is given by .

The total cost to produce one roll is $1,000. Find the total cost function C( x ). a.

b.

c.

d.

e.

____ 79. Use the given graph to estimate the left Riemann sum for the given interval with the stated number of subdivisions.

a. Left Sum = - 1 b. Left Sum = 1 c. Left Sum = - 2 d. Left Sum = 2 e. Left Sum = 0

____ 80. Calculate the Riemann Sum for the integral using n = 4.

a. 10 b. 8 c. 16 d. 14 e. 6

____ 81. The marginal cost function for the manufacture of portable CD players is given by where

is the number of CD players manufactured. Use a Riemann sun with n = 15 to estimate the cost of producing the first 15 CD players.

a. $148.95 b. $147.75 c. $147.90 d. $148.80

e. $133.88


a.

b.

c.

d.

e.


a.

b.

c.

d. e.


a.

b. c. d. e.


a. b. c. d. e.


a. b. c.

d.

e.

____ 87. Calculate the total area of the region bounded by the line , the and the lines and

a. 4,603 b. 4,347 c. 12,879 d. 4,185 e. 387

____ 88. A car traveling down a road has a velocity of mph at time hours. Find the total distance it travels from time hours to time hours. (Round your answer to the nearest mile.)

a. 216 miles b. 224 miles c. 206 miles

d. 218 miles e. 210 miles

____ 89. The way Professor Waner drives, he burns gas at the rate of gallons each hour, hours after a fill-up. Find the number of gallons of gas he burns in the first hours after a fill-up. Please round the answer to the nearest gallon.

a. 17 gallons b. 16 gallons c. 14 gallons d. 13 gallons e. 11 gallons

____ 90. The oxygen consumption of a bird embryo increases from the time the egg is laid through the time the chick hatches. In a typical galliform bird, the oxygen consumption, in milliliters per hour, can be approximated by

where t is time (in days) since the egg was laid. (An egg will typically hatch at around t = 28.) Find the total amount of oxygen consumed during the ninth and tenth days (t = 8 to t = 10).

a. 17 b. 457 c. 61 d. 1,131 e. 47


a. b. c. d. e.


a.

b.

c.

d.

e.


a. b. c. d. e.

____ 94. A rocket rising from the ground has a velocity of after t seconds. How far does it rise in

the first 3 minutes and 10 seconds?

a. b. c. d. e.

____ 95. Find the area of the region between for in .

a. b. c. d. e.

____ 96. Find the area of the region between and for in .

a.

b.

c. d.

e.

____ 97. Find the area of the region enclosed by and .

a.

b.

c. d.

e.

____ 98. Find the area of the region enclosed by and .

a.

b.

c.

d.

e.

____ 99. Find the area of the region enclosed by and the y-axis.

a. b. c. d. e.

____ 100. Suppose your annual income is dollars per year, where t represents the number of years since you began your job, while your annual expenses are dollars per year. Find the area between the graphs of and for .

a. Area = $129,900 b. Area = $197,100 c. Area = $67,200 d. Area = $62,700 e. Area = $65,400

____ 101. Find the average of the function over [ 0, 8 ].

a. Average =

b. Average = c. Average = d.

Average =

e. Average =

____ 102. Some values of a function and its 3-unit moving average are given. Supply the missing information: x 1 2 3 4 5 6 7 r( x ) 2 2 ? 8 ? 8 8 average undefined undefined 6 ? 11 ? ? a. x 1 2 3 4 5 6 7 r( x ) 2 2 14 8 11 8 8 average undefined undefined 6 8 11 9 9 b. x 1 2 3 4 5 6 7 r( x ) 2 2 14 8 11 8 8 average undefined undefined 6 8 11 12 12 c. x 1 2 3 4 5 6 7 r( x ) 2 2 15 8 10 8 12 average undefined undefined 6 8 11 9 9

____ 103. Calculate the 5-unit moving average of the given function.

a.

b.

c.

d.

e.

____ 104. If you invest $8,000 at 12% interest compounded continuously, what is the average amount in your account over one year? Round your answer to the nearest cent.

a. $8,302.51 b. $8,598.43 c. $8,499.79

d. $8,401.15 e. $8,697.07

____ 105. Calculate the producers' surplus at the unit price for the following supply equation.

a. $282.50 b. $283.50 c. $291.50 d. $285.50 e. $288.50

____ 106. Find the total value of the given income stream and also find its future value (at the end of the given interval) using the given interest rate.

a. TV = $2,000,000, FV = $–2,296,343.85 b. TV = $2,200,000, FV = $3,667,532.75 c. TV = $1,400,000, FV = $2,518,281.83 d. TV = $2,200,000, FV = $5,467,532.75 e. TV = $5,800,000, FV = $4,356,486.55

____ 107. Find the total value or the given income stream and also find its future value (at the end of the given interval) using the given interest rate.

a. TV = $2,234,000.03, FV = $1,411,333.34 b. TV=$2,234,000.03, FV=$4,729,378.11 c. TV = $4,234,000.03, FV = $314,911.04 d. TV = $4,468,000.07, FV = $657,058.77 e. TV = $67,020.00, FV = $13,161,504,599,350.49

____ 108. You are saving for your retirement by investing $700 per month in an annuity with a guaranteed interest rate of 6% per year. You increase the amount you invest at the rate of 4% per year. With continuous investment and compounding, how much will you have accumulated in the annuity by the time you retire in 25 years?

a. $7,406.31 b. $4,209,782.72 c. $740,631.04 d. $165,257.12 e. $38,218.71

____ 109. When your first child is born, you begin to save for college by depositing $700 per month in an account paying 12% interest per year. You increase the amount you save by 2% per year. With continuous investment and compounding, how much will you have accumulated in the account by the time your child enters college 18 years later?

a. $70,114.89

b. $607,975.89 c. $6,079.76 d. $5,945,936.09 e. $7,073.13

____ 110. The Megabucks Corporation is issuing a 5-year bond paying 8% interest. An investor wishes to buy the rights to receive the interest on $90,000 worth of these bonds and seeks a 6% rate of return. If the investor payments are made continuously, what will the investor pay?

a. $120,000.00 b. $281,983.06 c. $1,866.11 d. $31,101.81 e. $311.02

____ 111. Decide whether the integral. If the integral converges, compute its value.

a. converges to converges to b.

converges to

c. converges to

d. converges to e. diverges

____ 112. Decide whether the integral converges. If the integral converges, compute its value.

a. b. c. d. e.

____ 113. Decide whether the integral converges. If the integral converges, compute its value.

a.

b. c. d. e.

____ 114. Sales of the text "Calculus and You" have been declining continuously at an annual rate of 6%. Assuming that "Calculus and You" currently sell 6,000 copies per year and that sales will continue this pattern of decline, calculate total future sales of the text. Use the formula for continuously compounded interest with a negative rate.

a. 1,000,000 copies b. 100,000 copies c. 600,000 copies d. 2,500,000 copies e. 5,000,000 copies

Final_Review_210_Fa13 Answer Section

MULTIPLE CHOICE

1. ANS: B PTS: 1

2. ANS: D PTS: 1

3. ANS: C PTS: 1

4. ANS: E PTS: 1

5. ANS: A PTS: 1

6. ANS: A PTS: 1

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8. ANS: B PTS: 1

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10. ANS: B PTS: 1

11. ANS: E PTS: 1

12. ANS: C PTS: 1

13. ANS: B PTS: 1

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18. ANS: A PTS: 1

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20. ANS: B PTS: 1

21. ANS: A PTS: 1

22. ANS: C PTS: 1

23. ANS: B PTS: 1

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27. ANS: A PTS: 1

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30. ANS: C PTS: 1

31. ANS: D PTS: 1

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Final Review 210+Fa13 - Arizona State Universitydiane/Spring_2014/MAT_210/Final_Review... ·...

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