Question 1

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

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Question 2

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

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Question 3

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

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Question 4

Suppose that  and  . Find the following limit. ​  ​

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Question 5

Find the following limit if it exists:  . Use  when appropriate. ​

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Question 6

A petrol car is parked 35 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of  revolution per second. The rate at which the light beam moves along the wall is  ft/sec. Find the rate r when  is  . ​  ​

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Question 7

Determine the limit (if it exists). ​  ​

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Question 8

A petrol car is parked 65 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of  revolution per second. The rate at which the light beam moves along the wall is  ft/sec. Find the limit of r as  . ​  ​

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Question 9

Find the lmit. ​  ​

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...

Question 10

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

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Question 11

Find the limit. ​  ​

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...

Question 12

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.

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Question 13

A 30-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 18 feet. ​  ​

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Question 14

Use the rectangles in the following graph to approximate the area of the region bounded by  .  ​

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Question 15

Let  and  . Find the limit. ​  ​

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Question 16

Find the limit (if it exists). ​  ​

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Question 17

Find the limit. ​  ​

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...

Question 18

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

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Question 19

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 area of the shaded region bounded by the triangle with vertices (0,0), (7,8), (15,0).
​  ​

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Question 20

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

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Quiz 2: Limits and Their Properties

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

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

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

Suppose that and . Find the following limit.

Find the following limit if it exists: . Use when appropriate.

A petrol car is parked 35 feet from a long warehouse (see figure) . The revolving light on top of the car turns at a rate of revolution per second. The rate at which the light beam moves along the wall is ft/sec. Find the rate r when is .

Determine the limit (if it exists) .

A petrol car is parked 65 feet from a long warehouse (see figure) . The revolving light on top of the car turns at a rate of revolution per second. The rate at which the light beam moves along the wall is ft/sec. Find the limit of r as .

Find the lmit.

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

Find the limit.

A 30-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 18 feet.

Use the rectangles in the following graph to approximate the area of the region bounded by .

Let and . Find the limit.

Find the limit (if it exists) .

Find the limit.

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

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

Quiz 2: Limits and Their Properties

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

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

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

Suppose that and . Find the following limit. ​ ​

Find the following limit if it exists: . Use when appropriate. ​

A petrol car is parked 35 feet from a long warehouse (see figure) . The revolving light on top of the car turns at a rate of revolution per second. The rate at which the light beam moves along the wall is ft/sec. Find the rate r when is . ​ ​

Determine the limit (if it exists) . ​ ​

A petrol car is parked 65 feet from a long warehouse (see figure) . The revolving light on top of the car turns at a rate of revolution per second. The rate at which the light beam moves along the wall is ft/sec. Find the limit of r as . ​ ​

Find the lmit. ​ ​

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

Find the limit. ​ ​

Use the rectangles in the following graph to approximate the area of the region bounded by . ​

Let and . Find the limit. ​ ​

Find the limit (if it exists) . ​ ​

Find the limit. ​ ​

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

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

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

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

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

Suppose that and . Find the following limit.

Find the following limit if it exists: . Use when appropriate.

A petrol car is parked 35 feet from a long warehouse (see figure) . The revolving light on top of the car turns at a rate of revolution per second. The rate at which the light beam moves along the wall is ft/sec. Find the rate r when is .

Determine the limit (if it exists) .

A petrol car is parked 65 feet from a long warehouse (see figure) . The revolving light on top of the car turns at a rate of revolution per second. The rate at which the light beam moves along the wall is ft/sec. Find the limit of r as .

Find the lmit.

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

Find the limit.

Use the rectangles in the following graph to approximate the area of the region bounded by .

Let and . Find the limit.

Find the limit (if it exists) .

Find the limit.

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