Question 1

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

Accepted Answer

A)    
B)    
C)  0 
D)  3 
E)  2 
A)    
B)    
C)  0 
D)  3 
E)  2

Question 2

Suppose that   and   . Find the following limit. ​   ​

Accepted Answer

A)  -3 
B)  5 
C)  24 
D)  -11 
E)  0 
A)  -3 
B)  5 
C)  24 
D)  -11 
E)  0

Question 3

Find the limit. ​   ​

Accepted Answer

A)    
B)    
C)  -12 
D)  6 
E)  12 
A)    
B)    
C)  -12 
D)  6 
E)  12

Question 4

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

Accepted Answer

A)  5 
B) 16 
C) 1 
D) 4 
E)  does not exist. 
A)  5 
B) 16 
C) 1 
D) 4 
E)  does not exist.

Question 5

Find the limit. ​   ​

Accepted Answer

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

Question 6

Let   and   . Find the limit. ​   ​

Accepted Answer

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

Question 7

Let   and   . Find the limit. ​   ​

Accepted Answer

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

Question 8

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)  2, 2, 2, continuous 
B)  1, 1, 1, not continuous 
C)  2, 2, 2, not continuous 
D)  -4, -4, -4, continuous 
E)  1, 1, 1, continuous 
A)  2, 2, 2, continuous 
B)  1, 1, 1, not continuous 
C)  2, 2, 2, not continuous 
D)  -4, -4, -4, continuous 
E)  1, 1, 1, continuous

Question 9

Find the limit. ​   ​

Accepted Answer

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

Question 10

Find the limit. ​   ​

Accepted Answer

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

Question 11

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

Accepted Answer

A)  1 
B)  4 
C)  6 
D)  2 
E)  5 
A)  1 
B)  4 
C)  6 
D)  2 
E)  5

Question 12

A sphere has a volume of 4.0 cubic inches. If the sphere's volume can vary between 3.2 cubic inches and 5.5 cubic inches , how can the radius vary? Round your answer to five decimal places. ​

Accepted Answer

A)  Radius can vary between 0.91416 inch and 1.09503 inches. 
B)  Radius can vary between 1.45113 inches and 1.73825 inches. 
C)  Radius can vary between 0.18475 inch and 2.48475 inches. 
D)  Radius can vary between 1.58533 inches and 2.07839 inches. 
E)  Radius can vary between 0.87404 inch and 1.14587 inches. 
A)  Radius can vary between 0.91416 inch and 1.09503 inches. 
B)  Radius can vary between 1.45113 inches and 1.73825 inches. 
C)  Radius can vary between 0.18475 inch and 2.48475 inches. 
D)  Radius can vary between 1.58533 inches and 2.07839 inches. 
E)  Radius can vary between 0.87404 inch and 1.14587 inches.

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. ​   ​

Accepted Answer

A)  r =   ft/sec 
B)  r =   ft/sec 
C)      ft/sec 
D)  r =   ft/sec 
E)  r =   ft/sec 
A)  r =   ft/sec 
B)  r =   ft/sec 
C)      ft/sec 
D)  r =   ft/sec 
E)  r =   ft/sec

Question 14

Find all values of c such that f is continuous on (-∞,∞). ​   ​

Accepted Answer

A)  c = 2 
B)  c = 0 
C)    
D)    
E)    
A)  c = 2 
B)  c = 0 
C)    
D)    
E)

Question 15

Find the limit (if it exists). ​   ​

Accepted Answer

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

Question 16

Find the limit (if it exists). ​   ​

Accepted Answer

A)  Limit does not exist. 
B)  0 
C)  3 
D)  4 
E)  9 
A)  Limit does not exist. 
B)  0 
C)  3 
D)  4 
E)  9

Question 17

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

Accepted Answer

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

Question 18

Use the graph to find the limit. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  The limit does not exist. 
A)    
B)    
C)    
D)    
E)  The limit does not exist.

Question 19

Find the limit (if it exists). ​   ​

Accepted Answer

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

Question 20

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   . ​   ​

Accepted Answer

A)    ft/sec 
B)    ft/sec 
C)    ft/sec 
D)    ft/sec 
E)    ft/sec 
A)    ft/sec 
B)    ft/sec 
C)    ft/sec 
D)    ft/sec 
E)    ft/sec

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

Suppose that and . Find the following limit.

Find the limit.

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

Find the limit.

Let and . Find the limit.

Let and . 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.

Find the limit.

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

A sphere has a volume of 4.0 cubic inches. If the sphere's volume can vary between 3.2 cubic inches and 5.5 cubic inches , how can the radius vary? Round your answer to five decimal places.

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.

Find all values of c such that f is continuous on (-∞,∞).

Find the limit (if it exists).

Find the limit (if it exists).

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

Use the graph to find the limit.

Find the limit (if it exists).

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 .

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

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

Suppose that and . Find the following limit. ​ ​

Find the limit. ​ ​

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

Find the limit. ​ ​

Let and . Find the limit. ​ ​

Let and . 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. ​ ​

Find the limit. ​ ​

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

A sphere has a volume of 4.0 cubic inches. If the sphere's volume can vary between 3.2 cubic inches and 5.5 cubic inches , how can the radius vary? Round your answer to five decimal places. ​

Find all values of c such that f is continuous on (-∞,∞). ​ ​

Find the limit (if it exists). ​ ​

Find the limit (if it exists). ​ ​

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

Use the graph to find the limit. ​ ​

Find the limit (if it exists). ​ ​

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 . ​ ​

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

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

Suppose that and . Find the following limit.

Find the limit.

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

Find the limit.

Let and . Find the limit.

Let and . 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.

Find the limit.

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

A sphere has a volume of 4.0 cubic inches. If the sphere's volume can vary between 3.2 cubic inches and 5.5 cubic inches , how can the radius vary? Round your answer to five decimal places.

Find all values of c such that f is continuous on (-∞,∞).

Find the limit (if it exists).

Find the limit (if it exists).

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

Use the graph to find the limit.

Find the limit (if it exists).

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 .