Question 1

Use the graph to determine the following limits, and discuss the continuity of the function at x = -4. (i)  (ii)  (iii)  ​

Accepted Answer

A)  2, -2, does not exist, not continuous 
B)  2, 0, does not exist, not continuous 
C)  0, 2, does not exist, not continuous 
D)  -4, 0, does not exist, not continuous 
E)  0, 2, 0, continuous

Question 2

Discuss the continuity of the function  . ​

Accepted Answer

A)  f(x) is discontinuous at x= -2. 
B)  f(x) is discontinuous at x= -2, 2. 
C)  f(x) is discontinuous at x= 2. 
D)  f(x) is continuous for all real x. 
E)  f(x) is continuous at x= 4.

Question 3

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

Accepted Answer

A)  f(x) is not continuous at x = -2 and the discontinuity is nonremovable. 
B)  f(x) is not continuous at x = 0 and the discontinuity is removable. 
C)  f(x) is continuous for all real x. 
D)  f(x) is not continuous at x = -2 and the discontinuity is removable. 
E)  f(x) is not continuous at x = 0, 2 and x = 0 is a removable discontinuity.

Question 4

A long distance phone service charges $0.35 for the first 8 minutes and $0.05 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). ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 5

A ring has a inner circumference of 9 centimeters. If the ring's inner circumference can vary between 8.5 centimeters and 9.5 centimeters how can the radius vary? Round your answer to five decimal places. ​

Accepted Answer

A)  Radius can vary between 7.32046 centimeters and 9.14424 centimeters. 
B)  Radius can vary between 1.64488 centimeters and 1.73895 centimeters. 
C)  Radius can vary between 1.35282 centimeters and 1.51197 centimeters. 
D)  Radius can vary between 2.70563 centimeters and 3.02394 centimeters. 
E)  Radius can vary between 0.93239 centimeter and 1.93239 centimeters.

Question 6

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

Accepted Answer

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

Question 7

Consider the length of the graph of  from  to  . Approximate the length of the curve by finding the sum of the lengths of fiveline segments, as shown in following figure. Round your answer to two decimal places.  ​

Accepted Answer

A)  7.76 
B)  9.77 
C)  7.07 
D)  9.9 
E)  8.76

Question 8

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

Accepted Answer

A)  x = -2 
B)  x = 4 
C)  x = 0 
D)  x = 4, x = 0 
E)  no vertical asymptotes

Question 9

Complete the table and use the result to estimate the limit. ​

Accepted Answer

A)  -0.062500 
B)   0.067500 
C)  -0.192500 
D)   0.047500 
E)  -0.172500

Question 10

Complete the table and use the result to estimate the limit. ​  ​         ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 11

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

Accepted Answer

A)  4 
B) 1 
C)  0 
D)  3 
E)  does not exist.

Question 12

Find the limit. ​  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 13

Let  and  . Find the limit. ​  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 14

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

Accepted Answer

A)  1 
B)  -7 
C)  7 
D)  14 
E)  -14

Question 15

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)  x = -9 (not removable), x = -5 (removable) 
C)  x = -9 (removable), x = -5 (not removable) 
D)  no points of continuity 
E)  x = -9 (not removable), x = -5 (not removable)

Question 16

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

Accepted Answer

A)  x = 2 
B)  x = 6 
C)  x = -6 
D)  x = 12 
E)  x = -2

Question 17

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  wherexand  are measured in miles. Find the rate of change of elevation when x= 3.

Accepted Answer

A)  precalculus, 0.06 
B)  calculus, 0.18 
C)  calculus, 0.36 
D)  calculus, 0.06 
E)  precalculus, 0.18

Question 18

Find  where  . ​

Accepted Answer

A)  1. 
B)  4 
C)  -5 
D)  1 
E)  Limit does not exist.

Question 19

Suppose that  and  . Find the following limit. ​  ​

Accepted Answer

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

Question 20

Let  and  . Find the limit. ​  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Exam 2: Limits and Their Properties

Use the graph to determine the following limits, and discuss the continuity of the function at x = -4. (i) (ii) (iii)

Discuss the continuity of the function .

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

A long distance phone service charges $0.35 for the first 8 minutes and $0.05 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 ring has a inner circumference of 9 centimeters. If the ring's inner circumference can vary between 8.5 centimeters and 9.5 centimeters how can the radius vary? Round your answer to five decimal places.

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

Consider the length of the graph of from to . Approximate the length of the curve by finding the sum of the lengths of fiveline segments, as shown in following figure. Round your answer to two decimal places.

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

Complete the table and use the result to estimate the limit.

Complete the table and use the result to estimate the limit.

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

Find the limit.

Let and . Find the limit.

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

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

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

Find where .

Suppose that and . Find the following limit.

Let and . Find the limit.

Exam 2: Limits and Their Properties

Use the graph to determine the following limits, and discuss the continuity of the function at x = -4. (i) (ii) (iii) ​

Discuss the continuity of the function . ​

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

A long distance phone service charges $0.35 for the first 8 minutes and $0.05 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 ring has a inner circumference of 9 centimeters. If the ring's inner circumference can vary between 8.5 centimeters and 9.5 centimeters how can the radius vary? Round your answer to five decimal places. ​

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

Consider the length of the graph of from to . Approximate the length of the curve by finding the sum of the lengths of fiveline segments, as shown in following figure. Round your answer to two decimal places. ​

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

Complete the table and use the result to estimate the limit. ​

Complete the table and use the result to estimate the limit. ​ ​ ​

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

Find the limit. ​ ​

Let and . Find the limit. ​ ​

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

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

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

Find where . ​

Suppose that and . Find the following limit. ​ ​

Let and . Find the limit. ​ ​

Use the graph to determine the following limits, and discuss the continuity of the function at x = -4. (i) (ii) (iii)

Discuss the continuity of the function .

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

A long distance phone service charges $0.35 for the first 8 minutes and $0.05 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 ring has a inner circumference of 9 centimeters. If the ring's inner circumference can vary between 8.5 centimeters and 9.5 centimeters how can the radius vary? Round your answer to five decimal places.

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

Consider the length of the graph of from to . Approximate the length of the curve by finding the sum of the lengths of fiveline segments, as shown in following figure. Round your answer to two decimal places.

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

Complete the table and use the result to estimate the limit.

Complete the table and use the result to estimate the limit.

Find the limit.

Let and . Find the limit.

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

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

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

Find where .

Suppose that and . Find the following limit.

Let and . Find the limit.