MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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1 Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) A particle starts at x = and moves along the x-axis with velocity v(t) =. for time t. Where is the particle at t = 7? A) x =. B) x = 1. C)x =. D) x = 7 7 1) ) A particle moves with velocity v(t) = t + 7 find the distance traveled between t = 1 and t =. A) 1 B) C) D) 9 ) 3) A particle moves with velocity v(t) = t + 3 find the distance traveled between t = and t =. A) 13 B) 1 C)1 D) 17 3) Use a finite approximation to estimate the area of the region enclosed between the graph of f and the x-axis for a x b. ) f(x) = x, a =, b = Use LRAM with four rectangles of equal width. A) 9 B) C) D) ) ) f(x) = x, a = 1, b = Use RRAM with four rectangles of equal width. A) 9 B) 1 C) D) 3 ) ) f(x) = x, a = 3, b = 7 Use MRAM with four rectangles of equal width. A) 117 B) C)1 D) 1 ) 7) f(x) = 1 x, a = 1, b = 7) Use MRAM with two rectangles of equal width. A) B) 7 7 C) D) 1 7 ) f(x) = 9 - x, a = -3, b = 3 Use MRAM with two rectangles of equal width. A) B) 13. C). D). ) Use a calculator or computer program to solve the problem. 9) Use MRAM to estimate the area of the region enclosed between the graph of y = x - x and the x-axis for x ; n = 1. A) 1.33 B) C) D) ) 1) Use RAM to estimate the area of the region enclosed between the graph of f(x) = x - x + and the x-axis for x A) -.7 B).7 C) 1.7 D) 1.7 1) 1

2 11) Use RAM to estimate the area of the region enclosed between the graph of f(x) = 1 and the x-axis x 11) for 1 x 9 A).3 B).197 C).79 D).97 1) Use RAM to estimate the area of the region enclosed between the graph of f(x) = e-x and the x-axis for x 1 A).9 B).7 C).7 D). 1) 13) Use RAM to estimate the area of the region enclosed between the graph of f(x) = 7sin x and the x-axis for x π A) 7π B) 7 C) D) 1 13) 1) Use MRAM with n = to estimate the volume of a solid sphere of radius. A).97 B).33 C). D) 1. 1) Estimate the volume. 1) To estimate the volume of a solid hemisphere of radius 3, imagine its axis of symmetry to be the interval [, 3] on the x-axis. Partition [, 3] into subintervals of equal length and approximate the solid with cylinders based on the circular cross sections of the hemisphere perpendicular to the x-axis at the subintervals' right endpoints. A) 9.7 B) 3. C). D).7 1) 1) The nose "cone" of a rocket is a paraboloid obtained by revolving the curve y = x, x about the x-axis, where x is measured in feet. Estimate the volume of the nose cone by partitioning [, ] into subintervals of equal length, slicing the cone with planes perpendicular to the x-axis at the subintervals' midpoints, constructing cylinders of height 1 based on cross sections at these points, and finding the volumes of these cylinders. A).99 B) 3.19 C) D) )

3 Estimate the value of the quantity. 17) The table gives dye concentrations for a cardiac-output determination. The amount of dye injected was.9 mg. Plot the data and connect the data points with a smooth curve. Find the area under the curve using rectangles. Use this area to estimate the cardiac output. 17) Seconds Dye Conc. after (adjusted for injection recirculation) Dye concentration (mg/l) c 1 3 t Time (sec) A). L/min B) 1. L/min C) 39. L/min D) 9. L/min 3

4 1) The table gives dye concentrations for a cardiac-output determination. The amount of dye injected was. mg. Plot the data and connect the data points with a smooth curve. Find the area under the curve using rectangles. Use this area to estimate the cardiac output. 1) Seconds Dye Conc. after (adjusted for injection recirculation) Dye concentration (mg/l) c 1 3 t Time (sec) A) 1. L/min B).7 L/min C).1 L/min D).3 L/min 19) The table shows the velocity of a remote controlled race car moving along a dirt path for seconds. Estimate the distance traveled by the car using subintervals of length 1 with left-end point values. 19) (sec) (in./sec) A) 19 in. B) in. C)119 in. D) 13 in.

5 ) The table shows the velocity of a remote controlled race car moving along a dirt path for seconds. Estimate the distance traveled by the car using subintervals of length 1 with right-end point values. ) (sec) (in./sec) A) 17 in. B) 1 in. C)17 in. D) 1 in. 1) Joe wants to find out how far it is across the lake. His boat has a speedometer but no odometer. The table shows the boats velocity at 1 second intervals. Estimate the distance across the lake using right-end point values. 1) (sec) (ft/sec) A) 379 ft B) 379 ft C)7 ft D) 39 ft ) A piece of tissue paper is picked up in gusty wind. The table shows the velocity of the paper at second intervals. Estimate the distance the paper travelled using left-endpoints. ) (sec) (ft/sec) A) ft B) 1 ft C)1 ft D) ft

6 3) The velocity of a projectile fired straight into the air is given every half second. Use right endpoints to estimate the distance the projectile travelled in four seconds. 3) (sec) (m/sec) A). m B) 3. m C)7. m D) 3. m ) A hat is dropped from a hot air balloon. The hat falls faster and faster but its acceleration decreases over time due to air resistance. The acceleration is measured every second after the drop for seconds. Find an upper estimate for the speed when t = seconds. ) Time Acceleration (sec) (ft/sec) A) 7. ft/sec B) 19 ft/sec C) 3.3 ft/sec D) 3. ft/sec ) A swimming pool has a leak. The leak is getting worse. The following table gives the leakage rate every hours. Time Leakage (hr) (gal/hour) Give the upper estimate for the number of gallons lost. A). gallons B) 3. gallons C) 19. gallons D) 1. gallons )

7 ) A swimming pool has a leak. The leak is getting worse. The following table gives the leak rate every hours. Time Leakage (hr) (gal/hour) Suppose it keeps leaking. gallons every hours. After losing 3 gallons the leak is fixed. Approximately how long did the leak last? Use the right endpoints to estimate the first hours. A) 3. hours B). hours C) 9. hours D).7 hours ) 7

8 Answer Key Testname: UNTITLED1 1) B ) B 3) C ) B ) C ) D 7) B ) C 9) B 1) B 11) B 1) B 13) D 1) B 1) B 1) C 17) D 1) D 19) A ) A 1) A ) D 3) B ) A ) C ) C