Question 1

Let   .Determine the following limit. (Hint: Use the graph to calculate the limit.)

Accepted Answer

A) 2 
B) 0 
C) 4 
D) 6 
E) does not exist 
A) 2 
B) 0 
C) 4 
D) 6 
E) does not exist A

Question 2

Suppose that   and   . Find the following limit.

Accepted Answer

A) 4 
B) -1 
C) 9 
D) -20 
E) 5 
A) 4 
B) -1 
C) 9 
D) -20 
E) 5 D

Question 3

Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.A cyclist is riding on a path whose elevation is modeled by the function   where x and   are measured in miles. Find the rate of change of elevation when x = 4.5.

Accepted Answer

A) calculus , 0.21 
B) calculus , 0.09 
C) precalculus , 0.21 
D) precalculus , 0.09 
E) calculus , 0.81 
A) calculus , 0.21 
B) calculus , 0.09 
C) precalculus , 0.21 
D) precalculus , 0.09 
E) calculus , 0.81 E

Question 4

Discuss the continuity of the function   .

Accepted Answer

A)    is continuous for all real x. 
B)    is discontinuous at   . 
C)    is discontinuous at   . 
D)    is discontinuous at   . 
E)    is continuous at   . 
A)    is continuous for all real x. 
B)    is discontinuous at   . 
C)    is discontinuous at   . 
D)    is discontinuous at   . 
E)    is continuous at   .

Question 5

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 6

Suppose that   . Find the following limit.

Accepted Answer

A) -2 
B) 4 
C) 0 
D) 3 
E) 1 
A) -2 
B) 4 
C) 0 
D) 3 
E) 1

Question 7

Let   .Determine the following limit. (Hint: Use the graph to calculate the limit.)

Accepted Answer

A) 4 
B) 1 
C) 3 
D) 9 
E) does not exist. 
A) 4 
B) 1 
C) 3 
D) 9 
E) does not exist.

Question 8

Find the limit.

Accepted Answer

A) -26 
B)    
C) 26 
D)    
E) 13 
A) -26 
B)    
C) 26 
D)    
E) 13

Question 9

Find the limit.

Accepted Answer

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

Question 10

Find the limit (if it exists):

Accepted Answer

A) -32 
B)    
C)    
D) 8 
E)    
A) -32 
B)    
C)    
D) 8 
E)

Question 11

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 rate r when x is 20 feet.

Accepted Answer

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

Question 12

Let   and   . Find the limits:

Accepted Answer

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

Question 13

Determine the following limit. (Hint: Use the graph to calculate the limit.)

Accepted Answer

A) 0 
B) does not exist 
C) 4 
D) -4 
E) -8 
A) 0 
B) does not exist 
C) 4 
D) -4 
E) -8

Question 14

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

Accepted Answer

A) -11 
B) 10 
C) does not exist 
D) 11 
E) -10 
A) -11 
B) 10 
C) does not exist 
D) 11 
E) -10

Question 15

Find the limit (if it exists).   where

Accepted Answer

A) 10 
B) 0 
C) 27 
D) 9 
E) Limit does not exist. 
A) 10 
B) 0 
C) 27 
D) 9 
E) Limit does not exist.

Question 16

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

Accepted Answer

A) no points of discontinuity. 
B)    (not removable),   (removable) 
C)    (removable),   (not removable) 
D) no points of continuity. 
E)    (not removable),   (not removable) 
A) no points of discontinuity. 
B)    (not removable),   (removable) 
C)    (removable),   (not removable) 
D) no points of continuity. 
E)    (not removable),   (not removable)

Question 17

Find the limit.

Accepted Answer

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

Question 18

Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.Find the distance traveled in 14 seconds by an object traveling at a constant velocity of 12 feet per second.

Accepted Answer

A) precalculus , 336 ft 
B) precalculus , 168 ft 
C) calculus , 168 ft 
D) calculus , 336 ft 
E) calculus , 188 ft 
A) precalculus , 336 ft 
B) precalculus , 168 ft 
C) calculus , 168 ft 
D) calculus , 336 ft 
E) calculus , 188 ft

Question 19

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 20

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

Accepted Answer

A) 1 , 0 , does not exist , not continuous 
B) 0 , 1 , does not exist , not continuous 
C) 0 , 1 , 0 , continuous 
D) -3 , 0 , does not exist , not continuous 
E) 1 , -1 , does not exist , not continuous 
A) 1 , 0 , does not exist , not continuous 
B) 0 , 1 , does not exist , not continuous 
C) 0 , 1 , 0 , continuous 
D) -3 , 0 , does not exist , not continuous 
E) 1 , -1 , does not exist , not continuous

Let .Determine the following limit. (Hint: Use the graph to calculate the limit.)

Suppose that and . Find the following limit.

Discuss the continuity of the function .

Find the limit (if it exists).

Suppose that . Find the following limit.

Let .Determine the following limit. (Hint: Use the graph to calculate the limit.)

Find the limit.

Find the limit.

Find the limit (if it exists):

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 rate r when x is 20 feet.

Let and . Find the limits:

Determine the following limit. (Hint: Use the graph to calculate the limit.)

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

Find the limit (if it exists). where

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

Find the limit.

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

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

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

Let .Determine the following limit. (Hint: Use the graph to calculate the limit.)

Suppose that and . Find the following limit.

Discuss the continuity of the function .

Find the limit (if it exists).

Suppose that . Find the following limit.

Let .Determine the following limit. (Hint: Use the graph to calculate the limit.)

Find the limit.

Find the limit.

Find the limit (if it exists):

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 rate r when x is 20 feet.

Let and . Find the limits:

Determine the following limit. (Hint: Use the graph to calculate the limit.)

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

Find the limit (if it exists). where

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

Find the limit.

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

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

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