Question 1

Evaluate.   .

Accepted Answer

The answer of Evaluate.   ....

Question 2

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.

Accepted Answer

The relative increase in the surface are

Question 3

Answer true or false.

Accepted Answer

A) True 
 B)False

Question 4

Answer true or false. A plane is approaching an observer with a horizontal speed of 140ft/s and is currently 7,000ft from being directly overhead at an altitude of 12,000ft. The rate at which the angle of elevation, $\theta$ , is changing with respect to time, d$\theta$ /dt = (1/x)dy/dt. Where x is the horizontal distance and y is the altitude.

Accepted Answer

A) True 
 B)False

Question 5

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.

Accepted Answer

The surface area of the block is S = 6x<

Question 6

Use a differential to approximate sin 36°.

Accepted Answer

Let f(x) = sin x, x₀

Question 7

y = cos x. Find the formula for dy.

Accepted Answer

A)  dy = -sin (x + dx) 
B)  dy = -sin (x + dx) - sin x dx 
C)  dy = -sin x dx 
D)  dy = -sin (x + dx) + sin x dx 
E)  dy = -sin (x + dx) - sin dx 
A)  dy = -sin (x + dx) 
B)  dy = -sin (x + dx) - sin x dx 
C)  dy = -sin x dx 
D)  dy = -sin (x + dx) + sin x dx 
E)  dy = -sin (x + dx) - sin dx

Question 8

Answer true or false. If y = xcos x ,   .

Accepted Answer

A) True 
 B)False

Question 9

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.

Accepted Answer

The answer of The magnetic force F acting on a...

Question 10

y = ln(9x cos -1x). Find   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 11

Answer true or false.   .

Accepted Answer

A) True 
 B)False

Question 12

Answer true or false. If y = x8 - 7x, dy/dx = 7x.

Accepted Answer

A) True 
 B)False

Question 13

Gravitational force is inversely proportional to the distance between two objects squared. If F =   at a distance d = 3m, how fast is the force diminishing if the objects are moving away from each other at 1.2 m/s?

Accepted Answer

The answer of Gravitational force is inversely proportional to the...

Question 14

The power in watts for a circuit is given by P = I 2R. How fast is the power changing if the resistance, R, of the circuit is 900 $\Omega$, the current, I, is 7.7A, and the current is decreasing with respect to time at a rate of 0.025 A/s? (Assume the resistance is constant.)

Accepted Answer

The answer of The power in watts for a circuit...

Question 15

Find   if   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

Use a differential to approximate tan 41°.

Accepted Answer

Let f(x) = tan x , x₀

Question 17

If   , find   .

Accepted Answer

The answer of If   , find  ...

Question 18

Use a differential to approximate cos 65°.

Accepted Answer

Let f(x) = cos x, x₀

Question 19

Answer true or false. Suppose z = 3yx. Then dz/dt = 3x(dy/dt)+3y(dx/dt).

Accepted Answer

A) True 
 B)False

Question 20

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

Accepted Answer

dy = 4x³dx,

Evaluate. .

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.

Answer true or false.

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 sin 36°.

y = cos x. Find the formula for dy.

Answer true or false. If y = x^cos^x , .

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.

y = ln(9x cos ^-¹x). Find .

Answer true or false. .

Answer true or false. If y = x⁸ - 7x, dy/dx = 7x.

Gravitational force is inversely proportional to the distance between two objects squared. If F = at a distance d = 3m, how fast is the force diminishing if the objects are moving away from each other at 1.2 m/s?

The power in watts for a circuit is given by P = I ²R. How fast is the power changing if the resistance, R, of the circuit is 900 $\Omega$ , the current, I, is 7.7A, and the current is decreasing with respect to time at a rate of 0.025 A/s? (Assume the resistance is constant.)

Find if .

Use a differential to approximate tan 41°.

If , find .

Use a differential to approximate cos 65°.

Answer true or false. Suppose z = 3yx. Then dz/dt = 3x(dy/dt)+3y(dx/dt).

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

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

Exam 3: Topics in Deifferentiation

Evaluate. .

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.

Answer true or false.

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 sin 36°.

y = cos x. Find the formula for dy.

Answer true or false. If y = xcos x , .

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.

y = ln(9x cos -1x). Find .

Answer true or false. .

Answer true or false. If y = x8 - 7x, dy/dx = 7x.

Gravitational force is inversely proportional to the distance between two objects squared. If F = at a distance d = 3m, how fast is the force diminishing if the objects are moving away from each other at 1.2 m/s?

The power in watts for a circuit is given by P = I 2R. How fast is the power changing if the resistance, R, of the circuit is 900 Ω\OmegaΩ , the current, I, is 7.7A, and the current is decreasing with respect to time at a rate of 0.025 A/s? (Assume the resistance is constant.)

Find if .

Use a differential to approximate tan 41°.

If , find .

Use a differential to approximate cos 65°.

Answer true or false. Suppose z = 3yx. Then dz/dt = 3x(dy/dt)+3y(dx/dt).

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

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

Answer true or false. If y = x^cos^x , .

y = ln(9x cos ^-¹x). Find .

Answer true or false. If y = x⁸ - 7x, dy/dx = 7x.

The power in watts for a circuit is given by P = I ²R. How fast is the power changing if the resistance, R, of the circuit is 900 $\Omega$ , the current, I, is 7.7A, and the current is decreasing with respect to time at a rate of 0.025 A/s? (Assume the resistance is constant.)

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