Question 1

Differentiate.

Accepted Answer

The answer of Differentiate.  ...

Question 2

Select the correct Answer: for each question.
-Compute   and dy for the given values of   and

Accepted Answer

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

Question 3

If   Select the correct Answer

Accepted Answer

A)    
B)    
C)    
D)    
E)   
F)-11 
A)    
B)    
C)    
D)    
E)   
F)-11

Question 4

Use logarithmic differentiation to find the derivative of the function.

Accepted Answer

The answer of Use logarithmic differentiation to find the derivative...

Question 5

Use logarithmic differentiation to find the derivative of the function.

Accepted Answer

The answer of Use logarithmic differentiation to find the derivative...

Question 6

Find the derivative function.

Accepted Answer

The answer of Find the derivative function.  ...

Question 7

Select the correct Answer: for each question.
-Find an equation of the tangent line to the given curve at the indicated point.

Accepted Answer

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

Question 8

Gravel is being dumped from a conveyor belt at a rate of   and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal.How fast is the height of the pile increasing when the pile is   Round the result to the nearest hundredth.

Accepted Answer

The answer of Gravel is being dumped from a conveyor...

Question 9

Two curves are said to be orthogonal if their tangent lines are perpendicular at each point of intersection of the curves.Show that the curves of the given equations are orthogonal.

Accepted Answer

The curves

Question 10

Find an equation of the tangent line to the graph of the function at the indicated point.Select the correct Answer

Accepted Answer

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

Question 11

is the position of a body moving along a coordinate line;   is measured in feet and   in seconds, where   Find the position, velocity, and speed of the body at the indicated time.   t = 1

Accepted Answer

The answer of   is the position of a...

Question 12

Find the second derivative of the function.

Accepted Answer

The answer of Find the second derivative of the function....

Question 13

Two sides of a triangle are   and   in length and the angle between them is increasing at a rate of   Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is   Select the correct Answer

Accepted Answer

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

Question 14

Find the derivative of the function.

Accepted Answer

The answer of Find the derivative of the function. ...

Question 15

If $   is invested at 5% interest, find the value of   the investment at the end of 5 years if the interest is compounded annually.

Accepted Answer

The answer of If $   is invested at...

Question 16

Find the derivative of the function.

Accepted Answer

The answer of Find the derivative of the function. ...

Question 17

If u is a differentiable function of   and   then   Use this to find the derivative of the following function.Select the correct Answer

Accepted Answer

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

Question 18

Select the correct Answer: for each question.
-Find the tangent line to the ellipse   at the point

Accepted Answer

A)    
B)    
C)    
D)    
E)  None of these 
A)    
B)    
C)    
D)    
E)  None of these

Question 19

Select the correct Answer: for each question.
-Find the derivative of the function.

Accepted Answer

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

Question 20

Select the correct Answer for each question.
-Find equations of the tangent lines to the curve   that are parallel to the line

Accepted Answer

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

Differentiate.

Select the correct Answer: for each question. -Compute and dy for the given values of and

If Select the correct Answer

Use logarithmic differentiation to find the derivative of the function.

Use logarithmic differentiation to find the derivative of the function.

Find the derivative function.

Select the correct Answer: for each question. -Find an equation of the tangent line to the given curve at the indicated point.

Gravel is being dumped from a conveyor belt at a rate of and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal.How fast is the height of the pile increasing when the pile is Round the result to the nearest hundredth.

Two curves are said to be orthogonal if their tangent lines are perpendicular at each point of intersection of the curves.Show that the curves of the given equations are orthogonal.

Find an equation of the tangent line to the graph of the function at the indicated point.Select the correct Answer

is the position of a body moving along a coordinate line; is measured in feet and in seconds, where Find the position, velocity, and speed of the body at the indicated time. t = 1

Find the second derivative of the function.

Two sides of a triangle are and in length and the angle between them is increasing at a rate of Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is Select the correct Answer

Find the derivative of the function.

If $ is invested at 5% interest, find the value of the investment at the end of 5 years if the interest is compounded annually.

Find the derivative of the function.

If u is a differentiable function of and then Use this to find the derivative of the following function.Select the correct Answer

Select the correct Answer: for each question. -Find the tangent line to the ellipse at the point

Select the correct Answer: for each question. -Find the derivative of the function.

Select the correct Answer for each question. -Find equations of the tangent lines to the curve that are parallel to the line

Functions and Models

Limits and Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Filters

Exam 3: Differentiation Rules

Differentiate.

Select the correct Answer: for each question. -Compute and dy for the given values of and

If Select the correct Answer

Use logarithmic differentiation to find the derivative of the function.

Use logarithmic differentiation to find the derivative of the function.

Find the derivative function.

Select the correct Answer: for each question. -Find an equation of the tangent line to the given curve at the indicated point.

Gravel is being dumped from a conveyor belt at a rate of and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal.How fast is the height of the pile increasing when the pile is Round the result to the nearest hundredth.

Two curves are said to be orthogonal if their tangent lines are perpendicular at each point of intersection of the curves.Show that the curves of the given equations are orthogonal.

Find an equation of the tangent line to the graph of the function at the indicated point.Select the correct Answer

is the position of a body moving along a coordinate line; is measured in feet and in seconds, where Find the position, velocity, and speed of the body at the indicated time. t = 1

Find the second derivative of the function.

Two sides of a triangle are and in length and the angle between them is increasing at a rate of Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is Select the correct Answer

Find the derivative of the function.

If $ is invested at 5% interest, find the value of the investment at the end of 5 years if the interest is compounded annually.

Find the derivative of the function.

If u is a differentiable function of and then Use this to find the derivative of the following function.Select the correct Answer

Select the correct Answer: for each question. -Find the tangent line to the ellipse at the point

Select the correct Answer: for each question. -Find the derivative of the function.

Select the correct Answer for each question. -Find equations of the tangent lines to the curve that are parallel to the line

Functions and Models

Limits and Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Filters