Question 1

Find the limit (if it exists). ​   ​

Accepted Answer

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

Question 2

Suppose that   . Find the following limit. ​   ​

Accepted Answer

A)  -1 
B)  1 
C)  3 
D)  0 
E)  2 
A)  -1 
B)  1 
C)  3 
D)  0 
E)  2

Question 3

Find the limit (if it exists). ​   ​

Accepted Answer

A)  10 
B)    
C)    
D)    
E)    . 
A)  10 
B)    
C)    
D)    
E)    .

Question 4

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

Accepted Answer

A)  7 
B)  2 
C)  1 
D)  5 
E)  6 
A)  7 
B)  2 
C)  1 
D)  5 
E)  6

Question 5

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

Accepted Answer

A)  -109 
B)  119 
C)  -119 
D)  109 
E)  does not exist 
A)  -109 
B)  119 
C)  -119 
D)  109 
E)  does not exist

Question 6

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

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

Question 7

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

Accepted Answer

A)  a = 3, b = 0 
B)  a = 3, b = -3 
C)  a = -3, b = -3 
D)  a = -3, b = 3 
E)  a = 3, b = 3 
A)  a = 3, b = 0 
B)  a = 3, b = -3 
C)  a = -3, b = -3 
D)  a = -3, b = 3 
E)  a = 3, b = 3

Question 8

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

A)  calculus, 0.72 
B)  precalculus, 0.12 
C)  calculus, 0.12 
D)  precalculus, 0.72 
E)  precalculus, 0.37 
A)  calculus, 0.72 
B)  precalculus, 0.12 
C)  calculus, 0.12 
D)  precalculus, 0.72 
E)  precalculus, 0.37

Question 9

Find the limit. ​   ​

Accepted Answer

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

Question 10

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

Accepted Answer

A)  0.9481 
B)  1.8961 
C)  3.7922 
D)  1.4221 
E)  1.2704 
A)  0.9481 
B)  1.8961 
C)  3.7922 
D)  1.4221 
E)  1.2704

Question 11

Find the limit (if it exists). ​   ​

Accepted Answer

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

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

Accepted Answer

A)  precalculus , 120 
B)  calculus , 180 
C)  precalculus , 60 
D)  precalculus , 180 
E)  calculus , 120 
A)  precalculus , 120 
B)  calculus , 180 
C)  precalculus , 60 
D)  precalculus , 180 
E)  calculus , 120

Question 13

Suppose that   and   . Find the following limit. ​   ​

Accepted Answer

A)  0 
B)  -4 
C)  -9 
D)  -17 
E)  52 
A)  0 
B)  -4 
C)  -9 
D)  -17 
E)  52

Question 14

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.
​   ​

Accepted Answer

A)  calculus , 15 
B)  precalculus , 15 
C)  precalculus , 18 
D)  calculus , 22 
E)  precalculus , 22
​ 
A)  calculus , 15 
B)  precalculus , 15 
C)  precalculus , 18 
D)  calculus , 22 
E)  precalculus , 22
​

Question 15

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

Accepted Answer

A)    
B)  -4 
C)  1 
D)    
E)  does not exist 
A)    
B)  -4 
C)  1 
D)    
E)  does not exist

Question 16

Suppose that   and   . Find the following limit. ​   ​

Accepted Answer

A)  9 
B)  -3 
C)  -21 
D)  -12 
E)  108 
A)  9 
B)  -3 
C)  -21 
D)  -12 
E)  108

Question 17

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 12 seconds by an object traveling at a constant velocity of 20 feet per second.
​

Accepted Answer

A)  calculus, 240 ft 
B)  calculus, 260 ft 
C)  precalculus, 240 ft 
D)  calculus, 480 ft 
E)  precalculus, 480 ft 
A)  calculus, 240 ft 
B)  calculus, 260 ft 
C)  precalculus, 240 ft 
D)  calculus, 480 ft 
E)  precalculus, 480 ft

Question 18

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

Accepted Answer

A)  6 
B) 1 
C) 5 
D) 4 
E) does not exist 
A)  6 
B) 1 
C) 5 
D) 4 
E) does not exist

Question 19

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

Accepted Answer

A)  x = 1, 5 
B)  x = 1, 5, -4 
C)  x = -1, -5 
D)  x = 5 
E)  x = -5 
A)  x = 1, 5 
B)  x = 1, 5, -4 
C)  x = -1, -5 
D)  x = 5 
E)  x = -5

Question 20

Determine the limit (if it exists). ​   ​

Accepted Answer

A)  8 
B)  1 
C)  0 
D)  -2 
E)  does not exist 
A)  8 
B)  1 
C)  0 
D)  -2 
E)  does not exist

Find the limit (if it exists).

Suppose that . Find the following limit.

Find the limit (if it exists).

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

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

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

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

Find the limit.

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

Find the limit (if it exists).

Suppose that and . Find the following limit.

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

Suppose that and . Find the following limit.

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

Find all vertical asymptotes (if any) of the function

Determine 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

Find the limit (if it exists). ​ ​

Suppose that . Find the following limit. ​ ​

Find the limit (if it exists). ​ ​

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

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

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

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

Find the limit. ​ ​

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

Find the limit (if it exists). ​ ​

Suppose that and . Find the following limit. ​ ​

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

Suppose that and . Find the following limit. ​ ​

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

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

Determine 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

Find the limit (if it exists).

Suppose that . Find the following limit.

Find the limit (if it exists).

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

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

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

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

Find the limit.

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

Find the limit (if it exists).

Suppose that and . Find the following limit.

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

Suppose that and . Find the following limit.

Find all vertical asymptotes (if any) of the function

Determine the limit (if it exists).