Question 1

Use continuity to evaluate the limit.

Accepted Answer

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

Question 2

Use the graph to determine where the function is discontinuous.

Accepted Answer

A) At 0 
B) On the interval  
C) At  
D) At 1

Question 3

The monthly cost of driving a car depends on the number of miles driven. Julia found that in October it cost her  to drive  mi and in July it cost her  to drive  mi. Express the monthly cost C as a function of the distance driven d assuming that a linear relationship gives a suitable model.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 4

Find the limit  .

Accepted Answer

The answer of Find the limit  ....

Question 5

A box with an open top is to be constructed from a rectangular piece of card board with dimensions  in. by  in. by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a function of x.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 6

A tank holds  gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallons) after  minutes. If  is the point  on the graph of  , fill the table with the slopes of the secant lines  where Q is the point on the graph with the corresponding  .  Enter your answer to two decimal places.
t
Slope
5
10
20
25
30

Accepted Answer

The answer of A tank holds  gallons of water,...

Question 7

Find the limit.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 8

Use the graph of the function to find each limit.   ,  ,

Accepted Answer

The answer of Use the graph of the function to...

Question 9

The graphs of  and  are given.
a) For what values of  is  ?
b) Find the values of  and  .

Accepted Answer

The answer of The graphs of  and  are...

Question 10

Find the limit.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 11

Evaluate the limit.

Accepted Answer

The answer of Evaluate the limit. ...

Question 12

Use the graph of  to guess at the limit  , if it exists.

Accepted Answer

A) 1.3 
B) 0.8 
C) 0.2 
D) Does not exist

Question 13

Use the graph of the function to state the value of  , if it exists.

Accepted Answer

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

Question 14

The position of a car is given by the values in the following table.  Estimate the instantaneous velocity when  by averaging the velocities for the periods  .

Accepted Answer

The answer of The position of a car is given...

Question 15

Use a graph to find a number  such that  whenever  .

Accepted Answer

The answer of Use a graph to find a number...

Question 16

Find the limit.

Accepted Answer

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

Question 17

If  , evaluate the difference quotient  .

Accepted Answer

A)   
B)   
C) h 
D)   
E) None of these

Question 18

In the function  , what must be the value d, if  ?

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 19

Sketch the graph of the function f and evaluate

Accepted Answer

A)   3 
B)   -1 
C)   3 
D)   -1

Question 20

Choose an equation from the following that expresses the fact that a function  is continuous at the number  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Exam 1: Functions and Limits

Use continuity to evaluate the limit.

Use the graph to determine where the function is discontinuous.

The monthly cost of driving a car depends on the number of miles driven. Julia found that in October it cost her to drive mi and in July it cost her to drive mi. Express the monthly cost C as a function of the distance driven d assuming that a linear relationship gives a suitable model.

Find the limit .

A box with an open top is to be constructed from a rectangular piece of card board with dimensions in. by in. by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a function of x.

Find the limit.

Use the graph of the function to find each limit. , ,

The graphs of and are given. a) For what values of is ? b) Find the values of and .

Find the limit.

Evaluate the limit.

Use the graph of to guess at the limit , if it exists.

Use the graph of the function to state the value of , if it exists.

The position of a car is given by the values in the following table. Estimate the instantaneous velocity when by averaging the velocities for the periods .

Use a graph to find a number such that whenever .

Find the limit.

If , evaluate the difference quotient .

In the function , what must be the value d, if ?

Sketch the graph of the function f and evaluate

Choose an equation from the following that expresses the fact that a function is continuous at the number .