A particle moves according to s = t3. Find ds if t = 5 and dt = 4.

A) 75 B) 100 C) 300 D) 500 E) 60 A) 75 B) 100 C) 300 D) 500 E) 60

Exam 3: Topics in Deifferentiation

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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 81

Let . Find dy at x = 3 if dx = 0.032.

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Question 82

Evaluate.

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Question 83

y = ln(5x). For ,

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Question 84

Find if .

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Question 85

Find if .

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Question 86

Find if .

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Question 87

Answer true or false. Suppose z = 4yx. Then dz/dt = 4(dy/dt)(dx/dt).

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Question 88

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 89

Use a differential to approximate (2.97)⁵.

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Question 90

A particle moves according to s = t³. Find ds if t = 5 and dt = 4.

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Question 91

A straw is used to drink soda from the bottom of a cylindrical shaped cup. The diameter of the cup is 4 inches. The liquid is being consumed at the rate of 3 cubic inches per second. How fast is the level of the soda dropping?

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Question 92

Let $Let . Find \Delta y at x = 4 if \Delta x = 1.1.$ . Find $\Delta$ y at x = 4 if $\Delta$ x = 1.1.

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Question 93

Find the formula for dy if y = x⁶.

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Question 94

Approximate sin 30.075°.

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Question 95

Find dy/dx by differentiating implicitly. cos(xy³) = 4x

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Question 96

y = x⁶ log 3x. Find .

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Question 97

Evaluate.

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Question 98

Find if .

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Question 99

Answer true or false. If x² + y² = 3, .

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Question 100

Showing 81 - 100 of 171

Let . Find dy at x = 3 if dx = 0.032.

Evaluate.

y = ln(5x). For ,

Find if .

Find if .

Find if .

Answer true or false. Suppose z = 4yx. Then dz/dt = 4(dy/dt)(dx/dt).

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.

Use a differential to approximate (2.97)⁵.

A particle moves according to s = t³. Find ds if t = 5 and dt = 4.

A straw is used to drink soda from the bottom of a cylindrical shaped cup. The diameter of the cup is 4 inches. The liquid is being consumed at the rate of 3 cubic inches per second. How fast is the level of the soda dropping?

Let $Let . Find \Delta y at x = 4 if \Delta x = 1.1.$ . Find $\Delta$ y at x = 4 if $\Delta$ x = 1.1.

Find the formula for dy if y = x⁶.

Approximate sin 30.075°.

Find dy/dx by differentiating implicitly. cos(xy³) = 4x

y = x⁶ log 3x. Find .

Evaluate.

Find if .

Answer true or false. If x² + y² = 3, .

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Exam 3: Topics in Deifferentiation

Let . Find dy at x = 3 if dx = 0.032.

Evaluate.

y = ln(5x). For ,

Find if .

Find if .

Find if .

Answer true or false. Suppose z = 4yx. Then dz/dt = 4(dy/dt)(dx/dt).

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.

Use a differential to approximate (2.97)5.

A particle moves according to s = t3. Find ds if t = 5 and dt = 4.

A straw is used to drink soda from the bottom of a cylindrical shaped cup. The diameter of the cup is 4 inches. The liquid is being consumed at the rate of 3 cubic inches per second. How fast is the level of the soda dropping?

Let . Find Δ\DeltaΔ y at x = 4 if Δ\DeltaΔ x = 1.1.

Find the formula for dy if y = x6.

Approximate sin 30.075°.

Find dy/dx by differentiating implicitly. cos(xy3) = 4x

y = x6 log 3x. Find .

Evaluate.

Find if .

Answer true or false. If x2 + y2 = 3, .

Limits and Continuity

The Derivative

The Derivative in Graphing and Applications

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

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.

Use a differential to approximate (2.97)⁵.

A particle moves according to s = t³. Find ds if t = 5 and dt = 4.

Let $Let . Find \Delta y at x = 4 if \Delta x = 1.1.$ . Find $\Delta$ y at x = 4 if $\Delta$ x = 1.1.

Find the formula for dy if y = x⁶.

Find dy/dx by differentiating implicitly. cos(xy³) = 4x

y = x⁶ log 3x. Find .

Answer true or false. If x² + y² = 3, .