Question 1

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

Accepted Answer

A) 2 , 2 , 2 , not continuous 
B) 2 , 2 , 2 , continuous 
C) 3 , 3 , 3 , not continuous 
D) 3 , 3 , 3 , continuous 
E) -3 , -3 , -3 , continuous 
A) 2 , 2 , 2 , not continuous 
B) 2 , 2 , 2 , continuous 
C) 3 , 3 , 3 , not continuous 
D) 3 , 3 , 3 , continuous 
E) -3 , -3 , -3 , continuous

Question 2

Find the limit (if it exists).

Accepted Answer

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

Question 3

Find the limit.

Accepted Answer

A) -5 
B) 50 
C) -50 
D) 5 
E) 20 
A) -5 
B) 50 
C) -50 
D) 5 
E) 20

Question 4

Find the limit (if it exists).

Accepted Answer

A)    
B) 0 
C)    
D)    
E) Limit does not exist. 
A)    
B) 0 
C)    
D)    
E) Limit does not exist.

Question 5

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

Accepted Answer

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

Question 6

Let   and   . Find the limit.

Accepted Answer

A) -17 
B) 27 
C) 103 
D) -125 
E) 343 
A) -17 
B) 27 
C) 103 
D) -125 
E) 343

Question 7

Let   and   . Find the limit.

Accepted Answer

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

Question 8

Find the limit.

Accepted Answer

A) 0 
B)    
C) 1 
D) -1 
E)    
A) 0 
B)    
C) 1 
D) -1 
E)

Question 9

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

Accepted Answer

A) 4 
B) 3 
C) 10 
D) 11 
E) 9 
A) 4 
B) 3 
C) 10 
D) 11 
E) 9

Question 10

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

Accepted Answer

A) 4 , 4, 4, not continuous 
B) 2 , 2 , 2 , not continuous 
C) 1 , 1 , 1 , continuous 
D) 2 , 2 , 2 , continuous 
E) 1 , 1 , 1 , not continuous 
A) 4 , 4, 4, not continuous 
B) 2 , 2 , 2 , not continuous 
C) 1 , 1 , 1 , continuous 
D) 2 , 2 , 2 , continuous 
E) 1 , 1 , 1 , not continuous

Question 11

Find the limit.

Accepted Answer

A)    
B)    
C) 0 
D) -1 
E) 1 
A)    
B)    
C) 0 
D) -1 
E) 1

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

Find the limit (if it exists).

Find the limit.

Find the limit (if it exists).

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

Let and . Find the limit.

Let and . Find the limit.

Find the limit.

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

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

Find the limit.

Prerequisites

Functions and Their Graphs

Polynomial and Rational Functions

Differentiation

Applications of Differentiation

Integration

Exponential and Logarithmic Functions

Exponential and Logarithmic Functions and Calculus

Trigonometric Functions

Analytic Trigonometry

Trigonometric Functions and Calculus

Topics in Analytic Geometry

Additional Topics in Trigonometry

Filters

Exam 4: Limits and Their Properties

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

Find the limit (if it exists).

Find the limit.

Find the limit (if it exists).

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

Let and . Find the limit.

Let and . Find the limit.

Find the limit.

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

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

Find the limit.

Prerequisites

Functions and Their Graphs

Polynomial and Rational Functions

Differentiation

Applications of Differentiation

Integration

Exponential and Logarithmic Functions

Exponential and Logarithmic Functions and Calculus

Trigonometric Functions

Analytic Trigonometry

Trigonometric Functions and Calculus

Topics in Analytic Geometry

Additional Topics in Trigonometry

Filters