Question 1

If

Accepted Answer

The answer of If  ...

Question 2

A point moves along the curve   When the point is   at its x-coordinate is increasing at the rate of 2 units per second.How fast is its y-coordinate changing at that instant of time?

Accepted Answer

The answer of A point moves along the curve ...

Question 3

Determine the values of   for which the given linear approximation is accurate to within 0.07 at

Accepted Answer

The answer of Determine the values of   for...

Question 4

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

Accepted Answer

The answer of If   is a differentiable function...

Question 5

Differentiate the function.

Accepted Answer

The answer of Differentiate the function.  ...

Question 6

Select the correct Answer for each question.
-A curve passes through the point   and has the property that the slope of the curve at every   point is twice the   of   What is the equation of the curve?

Accepted Answer

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

Question 7

Find the derivative of the function.Select the correct Answer

Accepted Answer

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

Question 8

Select the correct Answer: for each question.
-Find the instantaneous rate of change of the function when

Accepted Answer

A)    
B) 3 
C) 9 
D)    
A)    
B) 3 
C) 9 
D)

Question 9

Two chemicals react to form another chemical.Suppose that the amount of chemical formed in time   (in hours) is given by   where   is measured in pounds.
a.Find the rate at which the chemical is formed when   Round to two decimal places.
b.How many pounds of the chemical are formed eventually?

Accepted Answer

a.0.08 lb/

Question 10

Find the derivative of the function.Select the correct Answer

Accepted Answer

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

Question 11

Select the correct Answer for each question.
-A plane flying horizontally at an altitude of 1 mi and a speed of   passes directly over a radar station.Find the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station.

Accepted Answer

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

Question 12

A turkey is removed from the oven when its temperature reaches   and is placed on a table in a room where the temperature is   After 10 minutes the temperature of the turkey is   and after 20 minutes it is   Use a linear approximation to predict the temperature of the turkey after   minutes.

Accepted Answer

The answer of A turkey is removed from the oven...

Question 13

Select the correct Answer: for each question.
-Differentiate the function.

Accepted Answer

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

Question 14

If   is the focal length of a convex lens and an object is placed at a distance v from the lens, then its image will be at a distance u from the lens, where   are related by the     Find the rate of change of with respect to

Accepted Answer

The answer of If   is the focal length...

Question 15

Differentiate.

Accepted Answer

The answer of Differentiate.  ...

Question 16

A telephone line hangs between two poles at 12 m apart in the shape of the catenary   where   and   are measured in meters.Find the slope of this curve where it meets the right pole.

Accepted Answer

The answer of A telephone line hangs between two poles...

Question 17

Find the derivative of the function.

Accepted Answer

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

Question 18

Select the correct Answer: for each question.
-Find an equation of the line tangent to the graph of   at the point where

Accepted Answer

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

Question 19

Differentiate.

Accepted Answer

The answer of Differentiate.  ...

Question 20

Select the correct Answer for each question.
-Find the given integral.

Accepted Answer

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

If

A point moves along the curve When the point is at its x-coordinate is increasing at the rate of 2 units per second.How fast is its y-coordinate changing at that instant of time?

Determine the values of for which the given linear approximation is accurate to within 0.07 at

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

Differentiate the function.

Select the correct Answer for each question. -A curve passes through the point and has the property that the slope of the curve at every point is twice the of What is the equation of the curve?

Find the derivative of the function.Select the correct Answer

Select the correct Answer: for each question. -Find the instantaneous rate of change of the function when

Two chemicals react to form another chemical.Suppose that the amount of chemical formed in time (in hours) is given by where is measured in pounds. a.Find the rate at which the chemical is formed when Round to two decimal places. b.How many pounds of the chemical are formed eventually?

Find the derivative of the function.Select the correct Answer

Select the correct Answer for each question. -A plane flying horizontally at an altitude of 1 mi and a speed of passes directly over a radar station.Find the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station.

A turkey is removed from the oven when its temperature reaches and is placed on a table in a room where the temperature is After 10 minutes the temperature of the turkey is and after 20 minutes it is Use a linear approximation to predict the temperature of the turkey after minutes.

Select the correct Answer: for each question. -Differentiate the function.

If is the focal length of a convex lens and an object is placed at a distance v from the lens, then its image will be at a distance u from the lens, where are related by the Find the rate of change of with respect to

Differentiate.

A telephone line hangs between two poles at 12 m apart in the shape of the catenary where and are measured in meters.Find the slope of this curve where it meets the right pole.

Find the derivative of the function.

Select the correct Answer: for each question. -Find an equation of the line tangent to the graph of at the point where

Differentiate.

Select the correct Answer for each question. -Find the given integral.

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

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Exam 3: Differentiation Rules

If

A point moves along the curve When the point is at its x-coordinate is increasing at the rate of 2 units per second.How fast is its y-coordinate changing at that instant of time?

Determine the values of for which the given linear approximation is accurate to within 0.07 at

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

Differentiate the function.

Select the correct Answer for each question. -A curve passes through the point and has the property that the slope of the curve at every point is twice the of What is the equation of the curve?

Find the derivative of the function.Select the correct Answer

Select the correct Answer: for each question. -Find the instantaneous rate of change of the function when

Two chemicals react to form another chemical.Suppose that the amount of chemical formed in time (in hours) is given by where is measured in pounds. a.Find the rate at which the chemical is formed when Round to two decimal places. b.How many pounds of the chemical are formed eventually?

Find the derivative of the function.Select the correct Answer

Select the correct Answer for each question. -A plane flying horizontally at an altitude of 1 mi and a speed of passes directly over a radar station.Find the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station.

A turkey is removed from the oven when its temperature reaches and is placed on a table in a room where the temperature is After 10 minutes the temperature of the turkey is and after 20 minutes it is Use a linear approximation to predict the temperature of the turkey after minutes.

Select the correct Answer: for each question. -Differentiate the function.

If is the focal length of a convex lens and an object is placed at a distance v from the lens, then its image will be at a distance u from the lens, where are related by the Find the rate of change of with respect to

Differentiate.

A telephone line hangs between two poles at 12 m apart in the shape of the catenary where and are measured in meters.Find the slope of this curve where it meets the right pole.

Find the derivative of the function.

Select the correct Answer: for each question. -Find an equation of the line tangent to the graph of at the point where

Differentiate.

Select the correct Answer for each question. -Find the given integral.

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