Deck 2: Section 4: Limits and Their Properties

Question 1

Use the graph as shown to determine the following limits, and discuss the continuity of the function at . (i) (ii) (iii)

A)
B) 2 , 2 , 2 ,
C)
D) 2 , 2 , 2 ,
E)

Answer 1

Question 2

Find the constant a such that the function is continuous on the entire real line.

A) 1
B)
C)
D)
E)

Answer 2

Question 3

Use the graph as shown to determine the following limits, and discuss the continuity of the function at . (i) (ii) (iii)

A)
B)
C)
D)
E)

Answer 3

Question 4

Find the limit (if it exists). Note that represents the greatest integer function.

A)
B)
C)
D)
E)

Question 5

A long distance phone service charges $ for the first minutes and $ for each additional minute or fraction thereof. Use the greatest integer function to write the cost C of a call in terms of time t (in minutes).

A)
B)
C)
D)
E)

Question 6

Find the constant a such that the function is continuous on the entire real line.

A)
B)
C)
D)
E)

Question 7

Find the limit (if it exists).

A)
B)
C)
D)
E)

Question 8

Discuss the continuity of the function .

A)
B)
C)
D)
E)

Question 9

Find the limit (if it exists).

A)
B)
C)
D)
E)

Question 10

Find all values of c such that is continuous on .

A)
B)
C)
D)
E)

Question 11

Find the x-values (if any) at which the function is not continuous. Which of the discontinuities are removable?

A)
B)
C)
D)
E)

Question 12

Find the limit (if it exists).

A)
B)
C)
D)
E)

Question 13

Find the x-values (if any) at which is not continuous.

A)
B)
C)
D)
E)

Question 14

Find the value of c guaranteed by the Intermediate Value Theorem.

A)
B)
C)
D)
E)

Question 15

Find the value of c guaranteed by the Intermediate Value Theorem.

A)
B)
C)
D)
E)

Question 16

Find the x-values (if any) at which the function is not continuous. Which of the discontinuities are removable?

A) 10 and - , removable
B) discontinuous everywhere
C) continuous everywhere
D) 10 and - , not removable
E) 0, removable

Question 17

Use the graph to determine the following limits, and discuss the continuity of the function at . (i) (ii) (iii)

A)
B)
C)
D)
E)

Question 18

Find the limit (if it exists). Note that represents the greatest integer function.

A)
B)
C)
D)
E)

Question 19

Find the x-values (if any) at which is not continuous.

A)
B)
C)
D)
E)

Question 20

Find the x-values (if any) at which the function is not continuous. Which of the discontinuities are removable?

A)
B)
C)
D)
E)