Question 1

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

Accepted Answer

Using a graphing utility, we can observe that the function approaches 1 from the left and 3 from the right as x approaches 2. Thus, the one-sided limit of the function as x approaches 2 is 3, which is only satisfied by choice D.

Question 2

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

B

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

D

Question 4

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

Accepted Answer

The answer of Find all the vertical asymptotes (if any)...

Question 5

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

The answer of A  -foot ladder is leaning against...

Question 6

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

Accepted Answer

The answer of Find the vertical asymptotes (if any) of...

Question 7

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

Accepted Answer

The answer of Find all the vertical asymptotes (if any)...

Question 8

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

Accepted Answer

The answer of Find all vertical asymptotes (if any) of...

Question 9

Find the limit.

Accepted Answer

The answer of Find the limit. 
...

Question 10

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

The answer of A petrol car is parked  feet...

Question 11

Find the limit.

Accepted Answer

The answer of Find the limit. 
...

Question 12

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

Accepted Answer

The answer of Find the vertical asymptotes (if any) of...

Question 13

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

Accepted Answer

The answer of Find the following limit if it exists:...

Question 14

Find the limit (if it exists).

Accepted Answer

The answer of Find the limit (if it exists). 
...

Question 15

Find the limit.

Accepted Answer

The answer of Find the limit. 
...

Question 16

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

The answer of A 25-foot ladder is leaning against a...

Question 17

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

Accepted Answer

The answer of Find all the vertical asymptotes (if any)...

Question 18

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

Accepted Answer

The answer of Use a graphing utility to graph the...

Quiz 2: Section 5 : Limits and Their Properties

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

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

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 .

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.

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

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

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

Find the limit.

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 .

Find the limit.

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

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

Find the limit (if it exists) .

Find the limit.

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 .

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

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