Question 1

Find the derivative of the algebraic function   . ​

Accepted Answer

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

Question 2

Evaluate the derivative of the function   at the point   . ​

Accepted Answer

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

Question 3

A spherical balloon is inflated with gas at the rate of 500 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is 40 centimeters? ​

Accepted Answer

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

Question 4

Apply Newton's Method to approximate the x-value of the indicated point of intersection of   and   . Continue the process until two successive approximations differ by less than 0.001.[Hint: Let  ]. Round your answer to three decimal places.

Accepted Answer

A)  8.993 
B)  5.494 
C)  7.993 
D)  4.494 
E)  9.429 
A)  8.993 
B)  5.494 
C)  7.993 
D)  4.494 
E)  9.429

Question 5

Find the slope of the graph of the function at the given value. ​   at   ​

Accepted Answer

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

Question 6

Use the rules of differentiation to find the derivative of the function   . ​

Accepted Answer

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

Question 7

Find the derivative of the function. ​   ​

Accepted Answer

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

Question 8

Find an equation of the tangent line to the graph of the function given below at the given point.   ,   (The coefficients below are given to two decimal places.) ​

Accepted Answer

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

Question 9

Use Newton's Method to approximate the zero(s) of the function   accurate to three decimal places. ​

Accepted Answer

A)  19.314 
B)  -19.346 
C)  19.251 
D)  -19.314 
E)  19.365 
A)  19.314 
B)  -19.346 
C)  19.251 
D)  -19.314 
E)  19.365

Question 10

Suppose the position function for a free-falling object on a certain planet is given by   . A silver coin is dropped from the top of a building that is 1,362 feet tall. Determine the average velocity of the coin over the time interval   . ​

Accepted Answer

A)  -53 ft/sec 
B)  16 ft/sec 
C)  48 ft/sec 
D)  -48 ft/sec 
E)  -16 ft/sec 
A)  -53 ft/sec 
B)  16 ft/sec 
C)  48 ft/sec 
D)  -48 ft/sec 
E)  -16 ft/sec

Question 11

Find the derivative of the function. ​   ​

Accepted Answer

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

Question 12

In a free-fall experiment, an object is dropped from a height of 256 feet. A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure. Assuming the object is released at time   . At what time will the object reach the ground level? ​   ​

Accepted Answer

A)  3 seconds 
B)  6 seconds 
C)  7 seconds 
D)  5 seconds 
E)  4 seconds 
A)  3 seconds 
B)  6 seconds 
C)  7 seconds 
D)  5 seconds 
E)  4 seconds

Question 13

Suppose that the total number of arrests T (in thousands) for all males ages 14 to 27 in 2006 is approximated by the model   ,   where x is the age in years (see figure). Approximate the two ages to one decimal place that had total arrests of 275 thousand. ​   ​

Accepted Answer

A)  15.7; 23.8 
B)  18.2; 21.6 
C)  16.7; 22.8 
D)  15.7; 22.8 
E)  16.7; 21.6 
A)  15.7; 23.8 
B)  18.2; 21.6 
C)  16.7; 22.8 
D)  15.7; 22.8 
E)  16.7; 21.6

Find the derivative of the algebraic function .

Evaluate the derivative of the function at the point .

A spherical balloon is inflated with gas at the rate of 500 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is 40 centimeters?

Apply Newton's Method to approximate the x-value of the indicated point of intersection of and . Continue the process until two successive approximations differ by less than 0.001.[Hint: Let ]. Round your answer to three decimal places.

Find the slope of the graph of the function at the given value. at

Use the rules of differentiation to find the derivative of the function .

Find the derivative of the function.

Find an equation of the tangent line to the graph of the function given below at the given point. , (The coefficients below are given to two decimal places.)

Use Newton's Method to approximate the zero(s) of the function accurate to three decimal places.

Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1,362 feet tall. Determine the average velocity of the coin over the time interval .

Find the derivative of the function.

In a free-fall experiment, an object is dropped from a height of 256 feet. A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure. Assuming the object is released at time . At what time will the object reach the ground level?

Suppose that the total number of arrests T (in thousands) for all males ages 14 to 27 in 2006 is approximated by the model , where x is the age in years (see figure). Approximate the two ages to one decimal place that had total arrests of 275 thousand.

Preparation for Calculus

Limits and Their Properties

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Exam 3: Differentiation

Find the derivative of the algebraic function . ​

Evaluate the derivative of the function at the point . ​

A spherical balloon is inflated with gas at the rate of 500 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is 40 centimeters? ​

Apply Newton's Method to approximate the x-value of the indicated point of intersection of and . Continue the process until two successive approximations differ by less than 0.001.[Hint: Let ]. Round your answer to three decimal places.

Find the slope of the graph of the function at the given value. ​ at ​

Use the rules of differentiation to find the derivative of the function . ​

Find the derivative of the function. ​ ​

Find an equation of the tangent line to the graph of the function given below at the given point. , (The coefficients below are given to two decimal places.) ​

Use Newton's Method to approximate the zero(s) of the function accurate to three decimal places. ​

Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1,362 feet tall. Determine the average velocity of the coin over the time interval . ​

Find the derivative of the function. ​ ​

In a free-fall experiment, an object is dropped from a height of 256 feet. A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure. Assuming the object is released at time . At what time will the object reach the ground level? ​ ​

Suppose that the total number of arrests T (in thousands) for all males ages 14 to 27 in 2006 is approximated by the model , where x is the age in years (see figure). Approximate the two ages to one decimal place that had total arrests of 275 thousand. ​ ​

Preparation for Calculus

Limits and Their Properties

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Find the derivative of the algebraic function .

Evaluate the derivative of the function at the point .

A spherical balloon is inflated with gas at the rate of 500 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is 40 centimeters?

Find the slope of the graph of the function at the given value. at

Use the rules of differentiation to find the derivative of the function .

Find the derivative of the function.

Find an equation of the tangent line to the graph of the function given below at the given point. , (The coefficients below are given to two decimal places.)

Use Newton's Method to approximate the zero(s) of the function accurate to three decimal places.

Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1,362 feet tall. Determine the average velocity of the coin over the time interval .

Find the derivative of the function.

In a free-fall experiment, an object is dropped from a height of 256 feet. A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure. Assuming the object is released at time . At what time will the object reach the ground level?

Suppose that the total number of arrests T (in thousands) for all males ages 14 to 27 in 2006 is approximated by the model , where x is the age in years (see figure). Approximate the two ages to one decimal place that had total arrests of 275 thousand.