Question 1

For the function   ,use a graphing utility to complete the table and estimate the limit as x approaches infinity. x
100
101
102
103
104
105
106   ​

Accepted Answer

A) 3 
B) -2 
C) 8 
D) 0 
E) None of the above 
A) 3 
B) -2 
C) 8 
D) 0 
E) None of the above E

Question 2

Find the point on the graph of the function   that is closest to the point   . ​

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

Sketch the graph of the relation   using any extrema,intercepts,symmetry,and asymptotes. ​

Accepted Answer

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

Question 5

​How many vertical asymptotes exist for the function   in the open interval   ? ​

Accepted Answer

A) ​4 
B) ​1 
C) ​2 
D) ​3 
A) ​4 
B) ​1 
C) ​2 
D) ​3

Question 6

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

Accepted Answer

A) 5 
B) 1 
C) 0 
D) 4 
E) does not exist 
A) 5 
B) 1 
C) 0 
D) 4 
E) does not exist

Question 7

Find the lmit. ​   ​

Accepted Answer

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

Question 8

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

Accepted Answer

A) 20 
B) -32 
C) 32 
D) -20 
E) does not exist 
A) 20 
B) -32 
C) 32 
D) -20 
E) does not exist

Question 9

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

Accepted Answer

A) 3,3,3,continuous 
B) 2,2,2,not continuous 
C) 3,3,3,not continuous 
D) -3,-3,-3,continuous 
E) 2,2,2,continuous 
A) 3,3,3,continuous 
B) 2,2,2,not continuous 
C) 3,3,3,not continuous 
D) -3,-3,-3,continuous 
E) 2,2,2,continuous

Question 10

A sphere has a volume of 2.92 cubic inches.What is the radius of the sphere? Round your answer to four decimal places. ​

Accepted Answer

A) 0.8867 inch 
B) 1.4075 inches 
C) 0.8349 inch 
D) 1.6698 inches 
E) 1.5144 inches 
A) 0.8867 inch 
B) 1.4075 inches 
C) 0.8349 inch 
D) 1.6698 inches 
E) 1.5144 inches

Question 11

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   .
​   ​

Accepted Answer

A) precalculus,0.09 
B) calculus,0.21 
C) calculus,0.81 
D) calculus,0.09 
E) precalculus,0.21 
A) precalculus,0.09 
B) calculus,0.21 
C) calculus,0.81 
D) calculus,0.09 
E) precalculus,0.21

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   where x and   are measured in miles.Find the rate of change of elevation when   .
​   ​

Accepted Answer

A) calculus,0.5 
B) precalculus,0.1 
C) calculus,0.1 
D) precalculus,0.5 
E) precalculus,0.35 
A) calculus,0.5 
B) precalculus,0.1 
C) calculus,0.1 
D) precalculus,0.5 
E) precalculus,0.35

Question 13

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

Accepted Answer

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

Question 14

A sphere has a volume of 4.32 cubic inches.If the sphere's volume can vary between 3.82 cubic inches and 6.42 cubic inches ,how can the radius vary? Round your answer to five decimal places. ​

Accepted Answer

A) Radius can vary between 0.96975 inch and 1.15296 inches. 
B) Radius can vary between 1.53938 inches and 1.83022 inches. 
C) Radius can vary between 0.51033 inch and 3.11033 inches. 
D) Radius can vary between 1.73211 inches and 2.24550 inches. 
E) Radius can vary between 0.95496 inch and 1.23801 inches. 
A) Radius can vary between 0.96975 inch and 1.15296 inches. 
B) Radius can vary between 1.53938 inches and 1.83022 inches. 
C) Radius can vary between 0.51033 inch and 3.11033 inches. 
D) Radius can vary between 1.73211 inches and 2.24550 inches. 
E) Radius can vary between 0.95496 inch and 1.23801 inches.

Question 15

Is   ​ continuous at   ? Explain why or why not.

Accepted Answer

@#IMG-DLM& . @#IMG-DLM& .
Therefore, @#IMG-DLM& does not exi

Question 16

Find the limit. ​   ​

Accepted Answer

A)    
B) -4 
C)    
D) 4 
E) -1 
A)    
B) -4 
C)    
D) 4 
E) -1

Question 17

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

Accepted Answer

A) 0.7850 
B) 1.5700 
C) 3.1400 
D) 1.1775 
E) 1.0519 
A) 0.7850 
B) 1.5700 
C) 3.1400 
D) 1.1775 
E) 1.0519

Question 18

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,5 
B) precalculus,5 
C) precalculus,6 
D) calculus,7 
E) precalculus,7 
A) calculus,5 
B) precalculus,5 
C) precalculus,6 
D) calculus,7 
E) precalculus,7

Question 19

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

Accepted Answer

A) 4 and -4,removable 
B) discontinuous everywhere 0 00 
C) continuous everywhere 0 00 
D) 4 and -4,not removable 
E) 0,removable 
A) 4 and -4,removable 
B) discontinuous everywhere 0 00 
C) continuous everywhere 0 00 
D) 4 and -4,not removable 
E) 0,removable

Question 20

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

Accepted Answer

A) 0 
B) 2 
C) 4 
D) 1 
E) 3 
A) 0 
B) 2 
C) 4 
D) 1 
E) 3

For the function ,use a graphing utility to complete the table and estimate the limit as x approaches infinity. x 10⁰ 10¹ 10² 10³ 10⁴ 10⁵ 10⁶

Find the point on the graph of the function that is closest to the point .

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

Sketch the graph of the relation using any extrema,intercepts,symmetry,and asymptotes.

How many vertical asymptotes exist for the function in the open interval ?

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

Find the lmit.

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

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

A sphere has a volume of 2.92 cubic inches.What is the radius of the sphere? Round your answer to four decimal places.

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

A sphere has a volume of 4.32 cubic inches.If the sphere's volume can vary between 3.82 cubic inches and 6.42 cubic inches ,how can the radius vary? Round your answer to five decimal places.

Is continuous at ? Explain why or why not.

Find the limit.

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

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.

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

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

Preparation for Calculus

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Exam 2: Limits and Their Properties

For the function ,use a graphing utility to complete the table and estimate the limit as x approaches infinity. x 100 101 102 103 104 105 106 ​

Find the point on the graph of the function that is closest to the point . ​

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

Sketch the graph of the relation using any extrema,intercepts,symmetry,and asymptotes. ​

​How many vertical asymptotes exist for the function in the open interval ? ​

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

Find the lmit. ​ ​

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

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