Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Find the equation of the tangent line T to the graph of 
at the given point 
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2.
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Find the equation of the tangent line T to the graph of 
at the given point 
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3.
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Compare dy and  for 
at x = –1 with  Give your answers to four decimal
places.
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4.
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Compare dy and  for 
at x = 0 with  Give your answers to four decimal
places.
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5.
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Find the differential dy of the function 
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6.
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Find the differential dy of the function  .
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7.
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Find the differential dy of the function  .
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8.
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The measurement of the side of a square floor tile is 14 inches, with a possible
error of  inch. Use differentials to approximate the
possible propagated error in computing the area of the square.
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9.
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The measurements of the base and altitude of a triangle are found to be 54 and
33 centimeters. The possible error in each measurement is 0.25 centimeter. Use differentials to
estimate the propagated error in computing the area of the triangle. Round your answer to four
decimal places.
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10.
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The measurement of the radius of the end of a log is found to be 28 inches, with
a possible error of  inch. Use differentials to approximate the
possible propagated error in computing the area of the end of the log.
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11.
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The radius of a spherical balloon is measured to be 8 inches, with a possible
error of 0.03 inch. Use differentials to approximate the maximum possible error in calculating the
volume of the sphere. Round your answer to two decimal places.
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12.
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The radius of a spherical balloon is measured to be 12 inches, with a possible
error of 0.06 inch. Use differentials to approximate the maximum possible error in calculating the
surface area of the sphere. Round your answer to two decimal places.
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13.
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The range R of a projectile is  where 
is the initial velocity in feet per second and  is the angle of elevation.
If  feet per second and 
is changed from  to  use differentials to
approximate the change in the range. Round your answer to the nearest integer. a. | 2,593 ft | b. | 4,568 ft | c. | 5,623
ft | d. | 2,811 ft | e. | 5,186 ft |
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14.
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Use differentials to approximate the value of  . Round your
answer to four decimal places. a. | 5.0000 | b. | 5.0100 | c. | 5.0400 | d. | 5.0200 | e. | 5.0300 |
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15.
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Use differentials to approximate the value of  . Round your
answer to four decimal places. a. | 1.9683 | b. | 1.9483 | c. | 1.9383 | d. | 1.9583 | e. | 1.9783 |
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