Question 1

Find the vertical asymptotes (if any) of the function  .

Accepted Answer

A)   
B)   
C)   
D)   
E)   B

Question 2

A petrol car is parked  feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of  revolution per second. The rate at which the light beam moves along the wall is  . Find the limit of r as  .

Accepted Answer

A)   
B)   
C)   
D)  65 
E)   A

Question 3

A petrol car is parked  feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of  revolution per second. The rate at which the light beam moves along the wall is  . Find the rate  when  is  .

Accepted Answer

A)   
B)   
C)   
D)   
E)   D

Question 4

Find all the vertical asymptotes (if any) of the graph of the function   .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 5

Determine whether  approaches  or  as x approaches  from the left and from the right by completing the tables below.   -3.1 -3.01
-3)001   -2.999
-2)99
-2)9
-2)5

Accepted Answer

A)   
B)   
C)   
D)

Question 6

Find all the vertical asymptotes (if any) of the graph of the function  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 7

Find the limit (if it exists).

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 8

Find all vertical asymptotes (if any) of the function  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 9

Use a graphing utility to graph the function  and determine the following one-sided limit.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 10

Find the vertical asymptotes (if any) of the function  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 11

Find all the vertical asymptotes (if any) of the graph of the function

Accepted Answer

A)   
B)   
C)   
D)   
E)  no vertical asymptotes

Question 12

Find the limit.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 13

A  -foot ladder is leaning against a house (see figure). If the base of the ladder is pulled away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of  , where x is the distance between the base of the ladder and the house. Find the rate r when x is  feet.

Accepted Answer

A)    ft/sec 
B)    ft/sec 
C)   
D)    ft/sec 
E)    ft/sec

Question 14

A 25-foot ladder is leaning against a house (see figure). If the base of the ladder is pulled away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of  where x is the distance between the base of the ladder and the house. Find the limit of r as  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 15

Use a graphing utility to graph the function  and determine the one-sided limit  .

Accepted Answer

A)   
B)   
C)  0 
D)   
E)  8

Question 16

Find the limit.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 17

Find the following limit if it exists:  . Use  when appropriate.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 18

Find the limit.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Exam 2: Section 5 : Limits and Their Properties

Find the vertical asymptotes (if any) of the function .

A petrol car is parked feet from a long warehouse (see figure) . The revolving light on top of the car turns at a rate of revolution per second. The rate at which the light beam moves along the wall is . Find the limit of r as .

A petrol car is parked feet from a long warehouse (see figure) . The revolving light on top of the car turns at a rate of revolution per second. The rate at which the light beam moves along the wall is . Find the rate when is .

Find all the vertical asymptotes (if any) of the graph of the function .

Determine whether approaches or as x approaches from the left and from the right by completing the tables below. -3.1 -3.01 -3) 001 -2.999 -2) 99 -2) 9 -2) 5

Find all the vertical asymptotes (if any) of the graph of the function .

Find the limit (if it exists) .

Find all vertical asymptotes (if any) of the function .

Use a graphing utility to graph the function and determine the following one-sided limit.

Find the vertical asymptotes (if any) of the function .

Find all the vertical asymptotes (if any) of the graph of the function

Find the limit.

A -foot ladder is leaning against a house (see figure) . If the base of the ladder is pulled away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of , where x is the distance between the base of the ladder and the house. Find the rate r when x is feet.

A 25-foot ladder is leaning against a house (see figure) . If the base of the ladder is pulled away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of where x is the distance between the base of the ladder and the house. Find the limit of r as .

Use a graphing utility to graph the function and determine the one-sided limit .

Find the limit.

Find the following limit if it exists: . Use when appropriate.

Find the limit.