Exam 4: Section 8: Applications of Differentiation

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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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The measurement of the side of a square floor tile is 14 inches, with a possible error of 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. inch. Use differentials to approximate the possible propagated error in computing the area of the square.

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Use differentials to approximate the value of Use differentials to approximate the value of   . Round your answer to four decimal places. . Round your answer to four decimal places.

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The range R of a projectile is 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. where 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. is the initial velocity in feet per second and 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. is the angle of elevation. If 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. feet per second and 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. is changed from 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. to 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. use differentials to approximate the change in the range. Round your answer to the nearest integer.

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Find the equation of the tangent line T to the graph of Find the equation of the tangent line T to the graph of   at the given point  at the given point Find the equation of the tangent line T to the graph of   at the given point

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Find the differential dy of the function Find the differential dy of the function   . .

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Compare dy and Compare dy and   for   at x = -1 with   Give your answers to four decimal places. for Compare dy and   for   at x = -1 with   Give your answers to four decimal places. at x = -1 with Compare dy and   for   at x = -1 with   Give your answers to four decimal places. Give your answers to four decimal places.

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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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Find the differential dy of the function Find the differential dy of the function

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Use differentials to approximate the value of Use differentials to approximate the value of   . Round your answer to four decimal places. . Round your answer to four decimal places.

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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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The total stopping distance T of a vehicle is The total stopping distance T of a vehicle is   where T is in feet and x is the speed in miles per hour. Use differentials to approximate the percent change in total stopping distance as speed changes from   to   miles per hour. Round your answer to one decimal place. where T is in feet and x is the speed in miles per hour. Use differentials to approximate the percent change in total stopping distance as speed changes from The total stopping distance T of a vehicle is   where T is in feet and x is the speed in miles per hour. Use differentials to approximate the percent change in total stopping distance as speed changes from   to   miles per hour. Round your answer to one decimal place. to The total stopping distance T of a vehicle is   where T is in feet and x is the speed in miles per hour. Use differentials to approximate the percent change in total stopping distance as speed changes from   to   miles per hour. Round your answer to one decimal place. miles per hour. Round your answer to one decimal place.

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Find the equation of the tangent line T to the graph of Find the equation of the tangent line T to the graph of   at the given point  at the given point Find the equation of the tangent line T to the graph of   at the given point

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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 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. inch. Use differentials to approximate the possible propagated error in computing the area of the end of the log.

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Find the differential dy of the function Find the differential dy of the function   . .

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Compare dy and Compare dy and   for   at x = 0 with   Give your answers to four decimal places. for Compare dy and   for   at x = 0 with   Give your answers to four decimal places. at x = 0 with Compare dy and   for   at x = 0 with   Give your answers to four decimal places. Give your answers to four decimal places.

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