Question 1

​Find an equation of the tangent line to the graph of   at the point (64,3). ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​none of the above 
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​none of the above

Question 2

​Determine whether the function below has any horizontal asymptotes. ​   ​

Accepted Answer

A)  ​horizontal asymptotes:   
B)  ​no horizontal asymptotes 
C)  ​horizontal asymptotes:   
D)  ​horizontal asymptotes:   
E)  ​​horizontal asymptotes:   
A)  ​horizontal asymptotes:   
B)  ​no horizontal asymptotes 
C)  ​horizontal asymptotes:   
D)  ​horizontal asymptotes:   
E)  ​​horizontal asymptotes:

Question 3

​Find the marginal profit for producing x units.(The profit is measured in dollars.) ​   ​

Accepted Answer

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

Question 4

​Sketch the graph of the function below.Choose a scale that allows all relative extrema and points of inflection to be identified on the graph. ​   ​   ​

Accepted Answer

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

Question 5

​Find   ​   ​

Accepted Answer

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

Question 6

A business has a cost (in dollars)of   for producing x units.What is the limit of   as x approaches infinity? ​

Accepted Answer

A)  ​∞ 
B)  ​$0.40 
C)  ​$900.40 
D)  ​$900.00 
E)  ​$899.60 
A)  ​∞ 
B)  ​$0.40 
C)  ​$900.40 
D)  ​$900.00 
E)  ​$899.60

Question 7

​Find   ,if   ​

Accepted Answer

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

Question 8

​Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 9

For   ,calculate   to three decimal places. ​

Accepted Answer

A)  1.609 
B)  24.142 
C)  7.828 
D)  0.600 
E)  4.828 
A)  1.609 
B)  24.142 
C)  7.828 
D)  0.600 
E)  4.828

Question 10

​Find all relative extrema of the function   Use the Second Derivative Test where applicable. ​

Accepted Answer

A)  ​relative max:   
B)  ​relative min:   
C)  ​no relative max or min 
D)  ​both A and B 
E)  ​none of the above 
A)  ​relative max:   
B)  ​relative min:   
C)  ​no relative max or min 
D)  ​both A and B 
E)  ​none of the above

Question 11

​Use the graph of   to identify at which of the indicated points the derivative   changes from positive to negative. ​
​   ​

Accepted Answer

A)  ​(5, 6) 
B)  ​(-1, 2), (2, 4) 
C)  ​(2, 4), (5, 6) 
D)  ​(2, 4) 
E)  ​(-1,2) 
A)  ​(5, 6) 
B)  ​(-1, 2), (2, 4) 
C)  ​(2, 4), (5, 6) 
D)  ​(2, 4) 
E)  ​(-1,2)

Question 12

​Find all relative extrema of the function   Use the Second Derivative Test where applicable. ​
​

Accepted Answer

A)  ​relative max:   ; no relative min 
B)  ​relative max:   ; no relative min 
C)  ​no relative max or min 
D)  ​relative min:   ; no relative max 
E)  ​​relative min:   ; no relative max 
A)  ​relative max:   ; no relative min 
B)  ​relative max:   ; no relative min 
C)  ​no relative max or min 
D)  ​relative min:   ; no relative max 
E)  ​​relative min:   ; no relative max

Question 13

​Find all relative extrema of the function   Use the Second-Derivative Test when applicable. ​

Accepted Answer

A)  ​The relative minimum is   and the relative maximum is   
B)  ​The relative maximum is   
C)  ​The relative minimum is   
D)  ​The relative maximum is   and the relative minima are   and   
E)  ​The relative minimum is   and the relative maximum is   
A)  ​The relative minimum is   and the relative maximum is   
B)  ​The relative maximum is   
C)  ​The relative minimum is   
D)  ​The relative maximum is   and the relative minima are   and   
E)  ​The relative minimum is   and the relative maximum is

Question 14

A graph of   is shown and a c-value is given.For this problem,use the graph to find     ​   ​

Accepted Answer

A)  6 
B)  1.5 
C)  -3 
D)  12 
E)  does not exist. 
A)  6 
B)  1.5 
C)  -3 
D)  12 
E)  does not exist.

Question 15

​Which of the following is the correct graph of   ? ​

Accepted Answer

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

Question 16

​Boat docking.Suppose that a boat is being pulled toward a dock by a winch that is 24 ft above the level of the boat deck.If the winch is pulling the cable at a rate of 13   ,at what rate is the boat approaching the dock when it is 32 ft from the dock? Use the figure below. ​   ​

Accepted Answer

A)  16.25​   
B)  13​   
C)  ​21.67   
D)  ​9.75   
E)  ​7.8   
A)  16.25​   
B)  13​   
C)  ​21.67   
D)  ​9.75   
E)  ​7.8

Question 17

Find any horizontal asymptotes for the given function. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  no horizontal asymptotes 
A)    
B)    
C)    
D)    
E)  no horizontal asymptotes

Question 18

​Find the differential dy of the function   ​

Accepted Answer

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

Question 19

Determine the following limit.(Hint: Use the graph of the function.) ​   ​
​   ​

Accepted Answer

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

Question 20

​If   ,is y a function of x? ​

Accepted Answer

A)  ​Yes 
B)  ​No 
A)  ​Yes 
B)  ​No

Find an equation of the tangent line to the graph of at the point (64,3).

Determine whether the function below has any horizontal asymptotes.

Find the marginal profit for producing x units.(The profit is measured in dollars.)

Sketch the graph of the function below.Choose a scale that allows all relative extrema and points of inflection to be identified on the graph.

Find

A business has a cost (in dollars)of for producing x units.What is the limit of as x approaches infinity?

Find ,if

Find the derivative of the following function.

For ,calculate to three decimal places.

Find all relative extrema of the function Use the Second Derivative Test where applicable.

Use the graph of to identify at which of the indicated points the derivative changes from positive to negative.

Find all relative extrema of the function Use the Second Derivative Test where applicable.

Find all relative extrema of the function Use the Second-Derivative Test when applicable.

A graph of is shown and a c-value is given.For this problem,use the graph to find

Which of the following is the correct graph of ?

Boat docking.Suppose that a boat is being pulled toward a dock by a winch that is 24 ft above the level of the boat deck.If the winch is pulling the cable at a rate of 13 ,at what rate is the boat approaching the dock when it is 32 ft from the dock? Use the figure below.

Find any horizontal asymptotes for the given function.

Find the differential dy of the function

Determine the following limit.(Hint: Use the graph of the function.)

If ,is y a function of x?

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

Exam 1: Functions, graphs, and Limits

​Find an equation of the tangent line to the graph of at the point (64,3). ​

​Determine whether the function below has any horizontal asymptotes. ​ ​

​Find the marginal profit for producing x units.(The profit is measured in dollars.) ​ ​

​Sketch the graph of the function below.Choose a scale that allows all relative extrema and points of inflection to be identified on the graph. ​ ​ ​

​Find ​ ​

A business has a cost (in dollars)of for producing x units.What is the limit of as x approaches infinity? ​

​Find ,if ​

​Find the derivative of the following function. ​ ​

For ,calculate to three decimal places. ​

​Find all relative extrema of the function Use the Second Derivative Test where applicable. ​

​Use the graph of to identify at which of the indicated points the derivative changes from positive to negative. ​ ​ ​

​Find all relative extrema of the function Use the Second Derivative Test where applicable. ​ ​

​Find all relative extrema of the function Use the Second-Derivative Test when applicable. ​

A graph of is shown and a c-value is given.For this problem,use the graph to find ​ ​

​Which of the following is the correct graph of ? ​

​Boat docking.Suppose that a boat is being pulled toward a dock by a winch that is 24 ft above the level of the boat deck.If the winch is pulling the cable at a rate of 13 ,at what rate is the boat approaching the dock when it is 32 ft from the dock? Use the figure below. ​ ​

Find any horizontal asymptotes for the given function. ​ ​

​Find the differential dy of the function ​

Determine the following limit.(Hint: Use the graph of the function.) ​ ​ ​ ​

​If ,is y a function of x? ​

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

Find an equation of the tangent line to the graph of at the point (64,3).

Determine whether the function below has any horizontal asymptotes.

Find the marginal profit for producing x units.(The profit is measured in dollars.)

Sketch the graph of the function below.Choose a scale that allows all relative extrema and points of inflection to be identified on the graph.

Find

A business has a cost (in dollars)of for producing x units.What is the limit of as x approaches infinity?

Find ,if

Find the derivative of the following function.

For ,calculate to three decimal places.

Find all relative extrema of the function Use the Second Derivative Test where applicable.

Use the graph of to identify at which of the indicated points the derivative changes from positive to negative.

Find all relative extrema of the function Use the Second Derivative Test where applicable.

Find all relative extrema of the function Use the Second-Derivative Test when applicable.

A graph of is shown and a c-value is given.For this problem,use the graph to find

Which of the following is the correct graph of ?

Boat docking.Suppose that a boat is being pulled toward a dock by a winch that is 24 ft above the level of the boat deck.If the winch is pulling the cable at a rate of 13 ,at what rate is the boat approaching the dock when it is 32 ft from the dock? Use the figure below.

Find any horizontal asymptotes for the given function.

Find the differential dy of the function

Determine the following limit.(Hint: Use the graph of the function.)

If ,is y a function of x?