Question 1

Suppose that  and  . Find the following limit. ​  ​

Accepted Answer

The answer of Suppose that  and  . Find...

Question 2

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

Accepted Answer

The answer of Determine the following limit.(Hint: Use the graph...

Question 3

Use the rectangles in the graph given below to approximate the area of the region bounded by  . Round your answer to three decimal places.  ​

Accepted Answer

The answer of Use the rectangles in the graph given...

Question 4

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

Accepted Answer

The answer of Use the graph as shown to determine...

Question 5

Find the limit. ​  ​

Accepted Answer

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

Question 6

Find the limit (if it exists). ​  ​

Accepted Answer

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

Question 7

Find the limit (if it exists). ​  ​

Accepted Answer

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

Question 8

Suppose that  and  . Find the following limit. ​  ​

Accepted Answer

The answer of Suppose that  and  . Find...

Question 9

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

Accepted Answer

The answer of Use the graph as shown to determine...

Question 10

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

Accepted Answer

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

Question 11

Find the limit (if it exists). ​  ​

Accepted Answer

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

Question 12

Find the limit. ​  ​

Accepted Answer

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

Question 13

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

Accepted Answer

The answer of Complete the table and use the result...

Question 14

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

Accepted Answer

The answer of Find the value of c guaranteed by...

Question 15

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 = 3.
​

Accepted Answer

The answer of Decide whether the following problem can be...

Question 16

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

Accepted Answer

As x approaches 2 from the left, the function approaches a limit of 4. As x approaches 2 from the right, the function also approaches a limit of 4. Therefore, the overall limit as x approaches 2 exists and is equal to 4.

Question 17

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

Accepted Answer

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

Question 18

Find the x-values (if any) at which the function f(x) = 11x² - 5x - 5 is not continuous. Which of the discontinuities are removable?

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

Find the limit. ​  ​

Accepted Answer

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

Quiz 2: Limits and Their Properties

Suppose that and . Find the following limit.

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

Use the rectangles in the graph given below to approximate the area of the region bounded by . Round your answer to three decimal places.

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

Find the limit.

Find the limit (if it exists) .

Find the limit (if it exists) .

Suppose that and . Find the following limit.

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

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

Find the limit (if it exists) .

Find the limit.

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

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

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

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

Find the x-values (if any) at which the function f(x) = 11x² - 5x - 5 is not continuous. Which of the discontinuities are removable?

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

Find the limit.

Quiz 2: Limits and Their Properties

Suppose that and . Find the following limit. ​ ​

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

Use the rectangles in the graph given below to approximate the area of the region bounded by . Round your answer to three decimal places. ​

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

Find the limit. ​ ​

Find the limit (if it exists) . ​ ​

Find the limit (if it exists) . ​ ​

Suppose that and . Find the following limit. ​ ​

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

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

Find the limit (if it exists) . ​ ​

Find the limit. ​ ​

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

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

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

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

Find the x-values (if any) at which the function f(x) = 11x2 - 5x - 5 is not continuous. Which of the discontinuities are removable? ​

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

Find the limit. ​ ​

Suppose that and . Find the following limit.

Use the rectangles in the graph given below to approximate the area of the region bounded by . Round your answer to three decimal places.

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

Find the limit.

Find the limit (if it exists) .

Find the limit (if it exists) .

Suppose that and . Find the following limit.

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

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

Find the limit (if it exists) .

Find the limit.

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

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

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

Find the x-values (if any) at which the function f(x) = 11x² - 5x - 5 is not continuous. Which of the discontinuities are removable?

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

Find the limit.