Question 1

Find the value of the constant A in y = A sin 3t so that d2y/dt2 + 7y = sin 3t.

Accepted Answer

A)    
B)    
C)    
D)  2 
E)  16 
A)    
B)    
C)    
D)  2 
E)  16

Question 2

Find f '(x) if f(x) = x4 cos x.

Accepted Answer

A)  4x3 cos x - x4 sin x 
B)  4x3 cos x 
C)  4x3 sin x 
D)  -4x3 cos x 
E)  -4x3 sin x 
A)  4x3 cos x - x4 sin x 
B)  4x3 cos x 
C)  4x3 sin x 
D)  -4x3 cos x 
E)  -4x3 sin x

Question 3

Answer true or false.   is differentiable everywhere.

Accepted Answer

A) True 
 B)False

Question 4

Find y''(x) if   .

Accepted Answer

The answer of Find y''(x) if   ....

Question 5

Find   if   .

Accepted Answer

The answer of Find   if   ....

Question 6

Find equations for the tangents and normals to the graph of y = 30 - x - x2 at the points where the curve intersects the x-axis.

Accepted Answer

@#IMG-DLM& So the tangent lines are:
At x = 5, the

Question 7

Show that   is continuous but not differentiable at x = 1.

Accepted Answer

Continuous: @#IMG-DLM& , so it is contin

Question 8

Find dy/dx if   .

Accepted Answer

A)    
B)    
C)  0 
D)  1 
E)    
A)    
B)    
C)  0 
D)  1 
E)

Question 9

Let   . Find the average rate of change of y with respect to x over the interval [4,7].

Accepted Answer

The answer of Let   . Find the average...

Question 10

Answer true or false. If y = sin x, d2y/dx2 = sin x.

Accepted Answer

A) True 
 B)False

Question 11

Find f '(x) if f(x) = 5x4.

Accepted Answer

A)  20x4 
B)  20x3 
C)  5x3 
D)  4x3 
E)    
A)  20x4 
B)  20x3 
C)  5x3 
D)  4x3 
E)

Question 12

Find f '(x) if   .

Accepted Answer

The answer of Find f '(x) if   ....

Question 13

Find f '(x) where f(x) = cos(tan 4x).

Accepted Answer

The answer of Find f '(x) where f(x) = cos(tan...

Question 14

Find f '(x) if   .

Accepted Answer

The answer of Find f '(x) if   ....

Question 15

Answer true or false. y = y''' + 5y' - 2 is satisfied by y = x.

Accepted Answer

A) True 
 B)False

Question 16

Find f '($\theta$) if   .

Accepted Answer

The answer of Find f '($\theta$) if   ....

Question 17

Given that f(1) = 5 and f '(1) = 6, find an equation for the tangent line to the graph of y = f(x) at the point where x = 1.

Accepted Answer

The answer of Given that f(1) = 5 and f...

Question 18

If y = x7 cos x, find dy/dx.

Accepted Answer

A)  7x6 cos x + x7 sin x 
B)  7x6 sin x - x7 cos x 
C)  42x5 cos x - 14x6 sin x - x7 cos x 
D)  42x5 cos x - 14x6 sin x 
E)  7x6 cos x - x7 sin x 
A)  7x6 cos x + x7 sin x 
B)  7x6 sin x - x7 cos x 
C)  42x5 cos x - 14x6 sin x - x7 cos x 
D)  42x5 cos x - 14x6 sin x 
E)  7x6 cos x - x7 sin x

Question 19

Given that f(1) = 5, f '(1) = 4 and g(x) = (f(x))-4, find g '(1).

Accepted Answer

The answer of Given that f(1) = 5, f '(1)...

Question 20

Let f(x) = ax3 + b, where a and b are constants. Use the method of Section 3.1 to show that the slope of the tangent to the graph of f at x = x0 is   .

Accepted Answer

Find the value of the constant A in y = A sin 3t so that d²y/dt² + 7y = sin 3t.

Find f '(x) if f(x) = x⁴ cos x.

Answer true or false. is differentiable everywhere.

Find y''(x) if .

Find if .

Find equations for the tangents and normals to the graph of y = 30 - x - x² at the points where the curve intersects the x-axis.

Show that is continuous but not differentiable at x = 1.

Find dy/dx if .

Let . Find the average rate of change of y with respect to x over the interval [4,7].

Answer true or false. If y = sin x, d²y/dx² = sin x.

Find f '(x) if f(x) = 5x⁴.

Find f '(x) if .

Find f '(x) where f(x) = cos(tan 4x).

Find f '(x) if .

Answer true or false. y = y''' + 5y' - 2 is satisfied by y = x.

Find f '( $\theta$ ) if $Find f '( \theta ) if .$ .

Given that f(1) = 5 and f '(1) = 6, find an equation for the tangent line to the graph of y = f(x) at the point where x = 1.

If y = x⁷ cos x, find dy/dx.

Given that f(1) = 5, f '(1) = 4 and g(x) = (f(x))^-⁴, find g '(1).

Let f(x) = ax³ + b, where a and b are constants. Use the method of Section 3.1 to show that the slope of the tangent to the graph of f at x = x₀ is .

Limits and Continuity

Topics in Deifferentiation

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 2: The Derivative

Find the value of the constant A in y = A sin 3t so that d2y/dt2 + 7y = sin 3t.

Find f '(x) if f(x) = x4 cos x.

Answer true or false. is differentiable everywhere.

Find y''(x) if .

Find if .

Find equations for the tangents and normals to the graph of y = 30 - x - x2 at the points where the curve intersects the x-axis.

Show that is continuous but not differentiable at x = 1.

Find dy/dx if .

Let . Find the average rate of change of y with respect to x over the interval [4,7].

Answer true or false. If y = sin x, d2y/dx2 = sin x.

Find f '(x) if f(x) = 5x4.

Find f '(x) if .

Find f '(x) where f(x) = cos(tan 4x).

Find f '(x) if .

Answer true or false. y = y''' + 5y' - 2 is satisfied by y = x.

Find f '( θ\thetaθ ) if .

Given that f(1) = 5 and f '(1) = 6, find an equation for the tangent line to the graph of y = f(x) at the point where x = 1.

If y = x7 cos x, find dy/dx.

Given that f(1) = 5, f '(1) = 4 and g(x) = (f(x))-4, find g '(1).

Let f(x) = ax3 + b, where a and b are constants. Use the method of Section 3.1 to show that the slope of the tangent to the graph of f at x = x0 is .

Limits and Continuity

Topics in Deifferentiation

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

Find the value of the constant A in y = A sin 3t so that d²y/dt² + 7y = sin 3t.

Find f '(x) if f(x) = x⁴ cos x.

Find equations for the tangents and normals to the graph of y = 30 - x - x² at the points where the curve intersects the x-axis.

Answer true or false. If y = sin x, d²y/dx² = sin x.

Find f '(x) if f(x) = 5x⁴.

Find f '( $\theta$ ) if $Find f '( \theta ) if .$ .

If y = x⁷ cos x, find dy/dx.

Given that f(1) = 5, f '(1) = 4 and g(x) = (f(x))^-⁴, find g '(1).

Let f(x) = ax³ + b, where a and b are constants. Use the method of Section 3.1 to show that the slope of the tangent to the graph of f at x = x₀ is .