Question 1

Determine the limit (if it exists). ​   ​

Accepted Answer

A)  0 
B)  56 
C)  11 
D)  28 
E)  does not exist 
A)  0 
B)  56 
C)  11 
D)  28 
E)  does not exist A

Question 2

A ring has a inner circumference of 2 centimeters. What is the radius of the ring? Round your answer to four decimal places. ​

Accepted Answer

A)  0.1592 centimeter 
B)  0.6366 centimeter 
C)  0.3183 centimeter 
D)  0.7979 centimeter 
E)  0.4053 centimeter 
A)  0.1592 centimeter 
B)  0.6366 centimeter 
C)  0.3183 centimeter 
D)  0.7979 centimeter 
E)  0.4053 centimeter C

Question 3

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

Accepted Answer

A)  10 and -10, removable 
B)  discontinuous everywhere 0 00 
C)  continuous everywhere 0 00 
D)  10 and -10, not removable 
E)  0, removable 
A)  10 and -10, removable 
B)  discontinuous everywhere 0 00 
C)  continuous everywhere 0 00 
D)  10 and -10, not removable 
E)  0, removable D

Question 4

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

Accepted Answer

A)  3.9485 
B)  2.6323 
C)  1.9742 
D)  1.4807 
E)  0.9871 
A)  3.9485 
B)  2.6323 
C)  1.9742 
D)  1.4807 
E)  0.9871

Question 5

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

Accepted Answer

A)  13 
B)  Limit does not exist. 
C)  12 
D)  0 
E)  11 
A)  13 
B)  Limit does not exist. 
C)  12 
D)  0 
E)  11

Question 6

Find the limit. ​   ​

Accepted Answer

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

Question 7

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

Accepted Answer

A)  x = -1 
B)  x = 5 
C)  x = 1, -1 
D)  x = 1 
E)  no vertical asymptotes 
A)  x = -1 
B)  x = 5 
C)  x = 1, -1 
D)  x = 1 
E)  no vertical asymptotes

Question 8

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

Accepted Answer

A)    
B)  6 
C)  -6 
D)    
E)  0 
A)    
B)  6 
C)  -6 
D)    
E)  0

Question 9

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

Accepted Answer

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

Question 10

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

A)  2.481 units2 
B)  6.371units2 
C)  3.585units2 
D)  6.872units2 
E)  6.903units2 
A)  2.481 units2 
B)  6.371units2 
C)  3.585units2 
D)  6.872units2 
E)  6.903units2

Question 11

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   . ​   ​

Accepted Answer

A)    
B)    
C)  0 
D)  65 
E)    
A)    
B)    
C)  0 
D)  65 
E)

Question 12

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

Accepted Answer

A)  5 
B)  3 
C)  1 
D)  0 
E)  does not exist. 
A)  5 
B)  3 
C)  1 
D)  0 
E)  does not exist.

Question 13

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 13 seconds by an object moving with a velocity of   feet per second.
​

Accepted Answer

A)  calculus, 162.3521 ft 
B)  precalculus, 163.7021 ft 
C)  calculus, 158.9412 ft 
D)  precalculus, 158.9412 ft 
E)  precalculus, 162.3521 ft 
A)  calculus, 162.3521 ft 
B)  precalculus, 163.7021 ft 
C)  calculus, 158.9412 ft 
D)  precalculus, 158.9412 ft 
E)  precalculus, 162.3521 ft

Question 14

Find the limit. ​   ​

Accepted Answer

A)  1 
B)  0 
C)  -1 
D)    
E)    
A)  1 
B)  0 
C)  -1 
D)    
E)

Question 15

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

Accepted Answer

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

Question 16

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

A)  x = 2, removable 
B)  x = 0, removable 
C)    
D)  continuous everywhere 
E)    
A)  x = 2, removable 
B)  x = 0, removable 
C)    
D)  continuous everywhere 
E)

Question 17

Determine the limit (if it exists). ​   ​

Accepted Answer

A)  0 
B)  1 
C)  2 
D)  ∞ 
E)  does not exist 
A)  0 
B)  1 
C)  2 
D)  ∞ 
E)  does not exist

Question 18

Find the limit. ​   ​

Accepted Answer

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

Question 19

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

A)  1, 1, 1, not continuous 
B)  2, 2, 2, continuous 
C)  1, 1, 1, continuous 
D)  2, 2, 2, not continuous 
E)  0, 0, 0, not continuous 
A)  1, 1, 1, not continuous 
B)  2, 2, 2, continuous 
C)  1, 1, 1, continuous 
D)  2, 2, 2, not continuous 
E)  0, 0, 0, not continuous

Question 20

Find the limit (if it exists). ​   ​

Accepted Answer

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

Determine the limit (if it exists).

A ring has a inner circumference of 2 centimeters. What is the radius of the ring? Round your answer to four decimal places.

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

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

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

Find the limit.

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

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

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 .

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

Find the limit.

Complete the table and use the result to estimate the 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?

Determine the limit (if it exists).

Find the 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 limit (if it exists).

Preparation for Calculus

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Exam 2: Limits and Their Properties

Determine the limit (if it exists). ​ ​

A ring has a inner circumference of 2 centimeters. What is the radius of the ring? Round your answer to four decimal places. ​

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

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

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

Find the limit. ​ ​

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

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

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 . ​ ​

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

Find the limit. ​ ​

Complete the table and use the result to estimate the 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? ​

Determine the limit (if it exists). ​ ​

Find the 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 limit (if it exists). ​ ​

Preparation for Calculus

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Determine the limit (if it exists).

A ring has a inner circumference of 2 centimeters. What is the radius of the ring? Round your answer to four decimal places.

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

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

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

Find the limit.

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

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

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 .

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

Find the limit.

Complete the table and use the result to estimate the 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?

Determine the limit (if it exists).

Find the 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 limit (if it exists).