Question 1

Use a differential to approximate  .

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Question 2

A circular hole 6 inches in diameter and 12 feet deep is to be drilled out of a glacier. The diameter of the hole is exact but the depth of the hole is measured with an error of ±1%. Estimate the percentage error in the volume of ice removed. (  is the volume of a cylinder of diameter d and height h.)

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Question 3

Use a differential to approximate cos 65°.

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Question 4

Use a differential to approximate sin 36°.

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Question 5

Let y = x⁴ and dx = 0.05 at x = 4. Find dy.

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Question 6

When a cubical block of metal is heated, each edge increases by 0.1% per degree increase in temperature. Use differentials to estimate the percentage increase in the surface area and volume of the block per degree increase in temperature.

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Question 7

Use a differential to approximate tan 41°.

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Question 8

Let  . Find $\Delta$y if$\Delta$x = 1 and the initial value of x is x = 1.

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Question 9

The surface area of a sphere is given by S = 4 $\pi$r² where r is the radius of the sphere. The radius is measured to be 6cm with an error of ±0.07cm. Use differentials to estimate the error in the calculated surface area.

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Question 10

When a spherical ball of metal is heated, the radius of the sphere increases by 0.3% per degree increase in temperature. Use differentials to estimate the percentage increase in the surface area and volume of the ball per degree increase in temperature.

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Question 11

The area of a circle is to be computed from a measured value of its diameter. Estimate the maximum permissible percentage error in the measurement if the percentage error in the area must be kept within 0.5%.

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Question 12

Use a differential to approximate  .

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Question 13

Let  . Find dy if dx = 2 and the initial value of x is x = 2.

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Question 14

The surface area S of a cube is to be computed from a measured value of its side x. Estimate the maximum permissible percentage error in the side measurement if the percentage error in the surface area must be kept to within ±1%.

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Question 15

Let y = 2x² and dx = 0.04 at x = 4. Find dy.

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Question 16

The magnetic force F acting on a particle is given by  , where r is the distance from the magnetic source and k is a constant. r is measured to be 4cm with a possible error of ±3%. Use differentials to estimate the error in the calculated value of F.

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Question 17

The magnetic force F acting on a particle is given by  , where r is the distance from the magnetic source and k is a constant. r is measured to be 2cm with a possible error of ±8%. Estimate the percentage error in F and r.

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Question 18

Find the formula for dy if y = x⁶.

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Question 19

The pressure P, the volume V, and the temperature T of an enclosed gas are related by the Ideal Gas Law, PV = kT where k is a constant. With the temperature held constant, the volume of the gas is calculated from a measured value of its pressure. Estimate the maximum permissible error in the pressure measurement if the percentage error in the volume must be kept to within ±3%.

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Question 20

Use a differential to approximate (2.97)⁵.

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Quiz 3: Topics in Deifferentiation

Use a differential to approximate .

Use a differential to approximate cos 65°.

Use a differential to approximate sin 36°.

Let y = x⁴ and dx = 0.05 at x = 4. Find dy.

When a cubical block of metal is heated, each edge increases by 0.1% per degree increase in temperature. Use differentials to estimate the percentage increase in the surface area and volume of the block per degree increase in temperature.

Use a differential to approximate tan 41°.

Let $Let . Find \Delta y if \Delta x = 1 and the initial value of x is x = 1.$ . Find $\Delta$ y if $\Delta$ x = 1 and the initial value of x is x = 1.

The surface area of a sphere is given by S = 4 $\pi$ r² where r is the radius of the sphere. The radius is measured to be 6cm with an error of ±0.07cm. Use differentials to estimate the error in the calculated surface area.

When a spherical ball of metal is heated, the radius of the sphere increases by 0.3% per degree increase in temperature. Use differentials to estimate the percentage increase in the surface area and volume of the ball per degree increase in temperature.

The area of a circle is to be computed from a measured value of its diameter. Estimate the maximum permissible percentage error in the measurement if the percentage error in the area must be kept within 0.5%.

Use a differential to approximate .

Let . Find dy if dx = 2 and the initial value of x is x = 2.

The surface area S of a cube is to be computed from a measured value of its side x. Estimate the maximum permissible percentage error in the side measurement if the percentage error in the surface area must be kept to within ±1%.

Let y = 2x² and dx = 0.04 at x = 4. Find dy.

The magnetic force F acting on a particle is given by , where r is the distance from the magnetic source and k is a constant. r is measured to be 4cm with a possible error of ±3%. Use differentials to estimate the error in the calculated value of F.

The magnetic force F acting on a particle is given by , where r is the distance from the magnetic source and k is a constant. r is measured to be 2cm with a possible error of ±8%. Estimate the percentage error in F and r.

Find the formula for dy if y = x⁶.

Use a differential to approximate (2.97)⁵.

Quiz 3: Topics in Deifferentiation

Use a differential to approximate .

Use a differential to approximate cos 65°.

Use a differential to approximate sin 36°.

Let y = x4 and dx = 0.05 at x = 4. Find dy.

When a cubical block of metal is heated, each edge increases by 0.1% per degree increase in temperature. Use differentials to estimate the percentage increase in the surface area and volume of the block per degree increase in temperature.

Use a differential to approximate tan 41°.

Let . Find Δ\DeltaΔ y if Δ\DeltaΔ x = 1 and the initial value of x is x = 1.

The surface area of a sphere is given by S = 4 π\piπ r2 where r is the radius of the sphere. The radius is measured to be 6cm with an error of ±0.07cm. Use differentials to estimate the error in the calculated surface area.

When a spherical ball of metal is heated, the radius of the sphere increases by 0.3% per degree increase in temperature. Use differentials to estimate the percentage increase in the surface area and volume of the ball per degree increase in temperature.

The area of a circle is to be computed from a measured value of its diameter. Estimate the maximum permissible percentage error in the measurement if the percentage error in the area must be kept within 0.5%.

Use a differential to approximate .

Let . Find dy if dx = 2 and the initial value of x is x = 2.

The surface area S of a cube is to be computed from a measured value of its side x. Estimate the maximum permissible percentage error in the side measurement if the percentage error in the surface area must be kept to within ±1%.

Let y = 2x2 and dx = 0.04 at x = 4. Find dy.

The magnetic force F acting on a particle is given by , where r is the distance from the magnetic source and k is a constant. r is measured to be 4cm with a possible error of ±3%. Use differentials to estimate the error in the calculated value of F.

The magnetic force F acting on a particle is given by , where r is the distance from the magnetic source and k is a constant. r is measured to be 2cm with a possible error of ±8%. Estimate the percentage error in F and r.

Find the formula for dy if y = x6.

Use a differential to approximate (2.97)5.

Let y = x⁴ and dx = 0.05 at x = 4. Find dy.

Let $Let . Find \Delta y if \Delta x = 1 and the initial value of x is x = 1.$ . Find $\Delta$ y if $\Delta$ x = 1 and the initial value of x is x = 1.

The surface area of a sphere is given by S = 4 $\pi$ r² where r is the radius of the sphere. The radius is measured to be 6cm with an error of ±0.07cm. Use differentials to estimate the error in the calculated surface area.

Let y = 2x² and dx = 0.04 at x = 4. Find dy.

Find the formula for dy if y = x⁶.

Use a differential to approximate (2.97)⁵.