Deck 2: Section 5 : Limits and Their Properties

Question 1

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

A)
B)
C)
D)
E)

Answer 1

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

A)
B)
C)
D)

Answer 2

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 .

A)
B)
C)
D)
E)

Answer 3

Question 4

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

A)
B)
C)
D)
E)

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.

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

Question 6

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

A)
B)
C)
D)
E)

Question 7

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

A)
B)
C)
D)
E)

Question 8

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

A)
B)
C)
D)
E)

Question 9

Find the limit.

A)
B)
C)
D)
E)

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 .

A)
B)
C)
D) 65
E)

Question 11

Find the limit.

A)
B)
C)
D)
E)

Question 12

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

A)
B)
C)
D)
E)

Question 13

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

A)
B)
C)
D)
E)

Question 14

Find the limit (if it exists).

A)
B)
C)
D)
E)

Question 15

Find the limit.

A)
B)
C)
D)
E)

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 .

A)
B)
C)
D)
E)

Question 17

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

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

Question 18

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

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