Question 1

Suppose that  . Find the following limit. ​  ​

Accepted Answer

B

Question 2

Find the limit (if it exists). ​  ​

Accepted Answer

D

Question 3

Suppose that  . Find the following limit. ​  ​

Accepted Answer

C

Question 4

Find the following limit (if it exists). Write a simpler function that agrees with the given function at all but one point. ​  7
​

Accepted Answer

The answer of Find the following limit (if it exists)....

Question 5

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

Accepted Answer

The answer of Use a graphing utility to graph the...

Question 6

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

The answer of A ring has a inner circumference of...

Question 7

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

Accepted Answer

The answer of Find the constant a and b such...

Question 8

Find the limit. ​  ​

Accepted Answer

The answer of Find the limit. ​  ​
...

Question 9

Find  where  . ​

Accepted Answer

The answer of Find  where  . ​
...

Question 10

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  . ​  ​

Accepted Answer

The answer of A 25-foot ladder is leaning against a...

Question 11

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

Accepted Answer

The answer of Find the vertical asymptotes (if any) of...

Question 12

A sphere has a volume of 4.12 cubic inches. What is the radius of the sphere? Round your answer to four decimal places. ​

Accepted Answer

To find the radius of the sphere, use the formula for the volume of a sphere: V = (4/3)πr^3. Solving for r, we get r = (3V/(4π))^(1/3). Plugging in V = 4.12, we find r ≈ 0.9945 inches.

Question 13

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

The answer of A long distance phone service charges $0.35...

Question 14

Suppose that  and  . Find the following limit. ​  ​

Accepted Answer

The answer of Suppose that  and  . Find...

Question 15

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

Accepted Answer

The answer of Find all the vertical asymptotes (if any)...

Question 16

Use the graph to find the limit. ​  ​

Accepted Answer

The answer of Use the graph to find the limit....

Question 17

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

Accepted Answer

The answer of Let  ​ Determine the following limit....

Question 18

Determine the limit (if it exists). ​  ​

Accepted Answer

The answer of Determine the limit (if it exists). ​...

Question 19

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

Accepted Answer

The answer of Find the x-values (if any) at which...

Question 20

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

Accepted Answer

The answer of Let  ​ Determine the following limit....

Quiz 2: Limits and Their Properties

Suppose that . Find the following limit.

Find the limit (if it exists) .

Suppose that . Find the following limit.

Find the following limit (if it exists) . Write a simpler function that agrees with the given function at all but one point. 7

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

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

Find the limit.

Find where .

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 .

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

A sphere has a volume of 4.12 cubic inches. What is the radius of the sphere? Round your answer to four decimal places.

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) .

Suppose that and . Find the following limit.

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

Use the graph to find the limit.

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

Determine the limit (if it exists) .

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

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

Quiz 2: Limits and Their Properties

Suppose that . Find the following limit. ​ ​

Find the limit (if it exists) . ​ ​

Suppose that . Find the following limit. ​ ​

Find the following limit (if it exists) . Write a simpler function that agrees with the given function at all but one point. ​ 7 ​

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

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

Find the limit. ​ ​

Find where . ​

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 . ​ ​

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

A sphere has a volume of 4.12 cubic inches. What is the radius of the sphere? Round your answer to four decimal places. ​

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) . ​

Suppose that and . Find the following limit. ​ ​

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

Use the graph to find the limit. ​ ​

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

Determine the limit (if it exists) . ​ ​

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

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

Suppose that . Find the following limit.

Find the limit (if it exists) .

Suppose that . Find the following limit.

Find the following limit (if it exists) . Write a simpler function that agrees with the given function at all but one point. 7

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

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

Find the limit.

Find where .

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 .

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

A sphere has a volume of 4.12 cubic inches. What is the radius of the sphere? Round your answer to four decimal places.

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) .

Suppose that and . Find the following limit.

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

Use the graph to find the limit.

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

Determine the limit (if it exists) .

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

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