Question 1

Find the point on the graph of the function   that is closest to the point   . Round all numerical values in your answer to four decimal places. ​

Accepted Answer

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

Question 2

Find the open interval(s) on which the function   is increasing in the interval   . Round numerical values in your answer to three decimal places. ​

Accepted Answer

A)  increasing on:   
B)  increasing on:   
C)  increasing on:   
D)  increasing on:   
E)  increasing on:   
A)  increasing on:   
B)  increasing on:   
C)  increasing on:   
D)  increasing on:   
E)  increasing on:

Question 3

A rectangle is bounded by the x- and y-axes and the graph of   (see figure). What length and width should the rectangle have so that its area is a maximum? ​   ​

Accepted Answer

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

Question 4

Analyze and sketch a graph of the function   . ​

Accepted Answer

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

Question 5

Find any critical numbers of the function   ,   . ​

Accepted Answer

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

Question 6

For the function   , use a graphing utility to complete the table and estimate the limit as x approaches infinity. ​

Accepted Answer

A)  0.5714 
B)  1.5714 
C)  1.7500 
D)  2.7500 
E)  0.7500 
A)  0.5714 
B)  1.5714 
C)  1.7500 
D)  2.7500 
E)  0.7500

Question 7

Find the limit. ​   ​

Accepted Answer

A)    
B)    
C)    
D)  -5 
E)    
A)    
B)    
C)    
D)  -5 
E)

Question 8

Locate the absolute extrema of the function   on the closed interval   . ​

Accepted Answer

A)  absolute max:   ; absolute min:   
B)  no absolute max; absolute min:   
C)  absolute max:   ; absolute min:   
D)  absolute max:   ; no absolute min 
E)  no absolute max or min 
A)  absolute max:   ; absolute min:   
B)  no absolute max; absolute min:   
C)  absolute max:   ; absolute min:   
D)  absolute max:   ; no absolute min 
E)  no absolute max or min

Question 9

Analyze and sketch a graph of the function   . ​

Accepted Answer

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

Question 10

A rectangular page is to contain 64 square inches of print. The margins on each side are 1 inch. Find the dimensions of the page such that the least amount of paper is used. ​

Accepted Answer

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

Question 11

Find the point on the graph of the function   that is closest to the point   . ​

Accepted Answer

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

Question 12

Determine whether Rolle's Theorem can be applied to the function   on the closed interval   . If Rolle's Theorem can be applied, find all numbers c in the open interval   such that   . ​

Accepted Answer

A)  Rolle's Theorem applies;   
B)  Rolle's Theorem applies;   
C)  Rolle's Theorem applies;   
D)  Rolle's Theorem applies;   
E)  Rolle's Theorem does not apply 
A)  Rolle's Theorem applies;   
B)  Rolle's Theorem applies;   
C)  Rolle's Theorem applies;   
D)  Rolle's Theorem applies;   
E)  Rolle's Theorem does not apply

Question 13

For the function   , use a graphing utility to complete the table and estimate the limit as x approaches infinity. x               f(x)
​

Accepted Answer

A)  -0.7500 
B)  0.5000 
C)  1.6800 
D)  -1.4000 
E)  does not exist 
A)  -0.7500 
B)  0.5000 
C)  1.6800 
D)  -1.4000 
E)  does not exist

Question 14

The height of an object t seconds after it is dropped from a height of 550 meters is   . Find the average velocity of the object during the first 11 seconds. ​

Accepted Answer

A)  53.90 m/sec 
B)  -53.90 m/sec 
C)  -121.00 m/sec 
D)  121.00 m/sec 
E)  -10.00 m/sec 
A)  53.90 m/sec 
B)  -53.90 m/sec 
C)  -121.00 m/sec 
D)  121.00 m/sec 
E)  -10.00 m/sec

Question 15

Find the limit. ​   ​

Accepted Answer

A)    
B)    
C)    
D)  -7 
E)    
A)    
B)    
C)    
D)  -7 
E)

Question 16

Identify the open intervals where the function   is increasing or decreasing. ​

Accepted Answer

A)  decreasing:   ; increasing:   
B)  decreasing on   
C)  increasing:   ; decreasing:   
D)  increasing:   ; decreasing:   
E)  increasing:   ; decreasing:   
A)  decreasing:   ; increasing:   
B)  decreasing on   
C)  increasing:   ; decreasing:   
D)  increasing:   ; decreasing:   
E)  increasing:   ; decreasing:

Question 17

Find the limit. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  does not exist 
A)    
B)    
C)    
D)    
E)  does not exist

Question 18

Identify the open intervals where the function   is increasing or decreasing. ​

Accepted Answer

A)  decreasing on   
B)  increasing on   
C)    
D)  decreasing on   ; increasing on   
E)    
A)  decreasing on   
B)  increasing on   
C)    
D)  decreasing on   ; increasing on   
E)

Question 19

Sketch a graph of the function   over the interval   . ​

Accepted Answer

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

Question 20

Find all critical numbers of the function   . ​

Accepted Answer

A)  critical numbers:   ,   ,   
B)  critical numbers:   ,   ,   
C)  critical numbers:   ,   
D)  critical numbers:   ,   
E)  no critical numbers 
A)  critical numbers:   ,   ,   
B)  critical numbers:   ,   ,   
C)  critical numbers:   ,   
D)  critical numbers:   ,   
E)  no critical numbers

Find the point on the graph of the function that is closest to the point . Round all numerical values in your answer to four decimal places.

Find the open interval(s) on which the function is increasing in the interval . Round numerical values in your answer to three decimal places.

A rectangle is bounded by the x- and y-axes and the graph of (see figure). What length and width should the rectangle have so that its area is a maximum?

Analyze and sketch a graph of the function .

Find any critical numbers of the function , .

For the function , use a graphing utility to complete the table and estimate the limit as x approaches infinity.

Find the limit.

Locate the absolute extrema of the function on the closed interval .

Analyze and sketch a graph of the function .

A rectangular page is to contain 64 square inches of print. The margins on each side are 1 inch. Find the dimensions of the page such that the least amount of paper is used.

Find the point on the graph of the function that is closest to the point .

Determine whether Rolle's Theorem can be applied to the function on the closed interval . If Rolle's Theorem can be applied, find all numbers c in the open interval such that .

For the function , use a graphing utility to complete the table and estimate the limit as x approaches infinity. x f(x)

The height of an object t seconds after it is dropped from a height of 550 meters is . Find the average velocity of the object during the first 11 seconds.

Find the limit.

Identify the open intervals where the function is increasing or decreasing.

Find the limit.

Identify the open intervals where the function is increasing or decreasing.

Sketch a graph of the function over the interval .

Find all critical numbers of the function .

Preparation for Calculus

Limits and Their Properties

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 4: Applications of Differentiation

Find the point on the graph of the function that is closest to the point . Round all numerical values in your answer to four decimal places. ​

Find the open interval(s) on which the function is increasing in the interval . Round numerical values in your answer to three decimal places. ​

A rectangle is bounded by the x- and y-axes and the graph of (see figure). What length and width should the rectangle have so that its area is a maximum? ​ ​

Analyze and sketch a graph of the function . ​

Find any critical numbers of the function , . ​

For the function , use a graphing utility to complete the table and estimate the limit as x approaches infinity. ​

Find the limit. ​ ​

Locate the absolute extrema of the function on the closed interval . ​

Analyze and sketch a graph of the function . ​

A rectangular page is to contain 64 square inches of print. The margins on each side are 1 inch. Find the dimensions of the page such that the least amount of paper is used. ​

Find the point on the graph of the function that is closest to the point . ​

Determine whether Rolle's Theorem can be applied to the function on the closed interval . If Rolle's Theorem can be applied, find all numbers c in the open interval such that . ​

For the function , use a graphing utility to complete the table and estimate the limit as x approaches infinity. x f(x) ​

The height of an object t seconds after it is dropped from a height of 550 meters is . Find the average velocity of the object during the first 11 seconds. ​

Find the limit. ​ ​

Identify the open intervals where the function is increasing or decreasing. ​

Find the limit. ​ ​

Identify the open intervals where the function is increasing or decreasing. ​

Sketch a graph of the function over the interval . ​

Find all critical numbers of the function . ​

Preparation for Calculus

Limits and Their Properties

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 point on the graph of the function that is closest to the point . Round all numerical values in your answer to four decimal places.

Find the open interval(s) on which the function is increasing in the interval . Round numerical values in your answer to three decimal places.

A rectangle is bounded by the x- and y-axes and the graph of (see figure). What length and width should the rectangle have so that its area is a maximum?

Analyze and sketch a graph of the function .

Find any critical numbers of the function , .

For the function , use a graphing utility to complete the table and estimate the limit as x approaches infinity.

Find the limit.

Locate the absolute extrema of the function on the closed interval .

Analyze and sketch a graph of the function .

A rectangular page is to contain 64 square inches of print. The margins on each side are 1 inch. Find the dimensions of the page such that the least amount of paper is used.

Find the point on the graph of the function that is closest to the point .

Determine whether Rolle's Theorem can be applied to the function on the closed interval . If Rolle's Theorem can be applied, find all numbers c in the open interval such that .

For the function , use a graphing utility to complete the table and estimate the limit as x approaches infinity. x f(x)

The height of an object t seconds after it is dropped from a height of 550 meters is . Find the average velocity of the object during the first 11 seconds.

Find the limit.

Identify the open intervals where the function is increasing or decreasing.

Find the limit.

Identify the open intervals where the function is increasing or decreasing.

Sketch a graph of the function over the interval .

Find all critical numbers of the function .