Question 1

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

Accepted Answer

A) 1 
B) 3 
C) Does not exist 
D) -2 
A) 1 
B) 3 
C) Does not exist 
D) -2

Question 2

The graph of the function   has been compressed horizontally by a factor of 3. Find the function for the transformed graph.

Accepted Answer

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

Question 3

Evaluate the limit, if it exists.

Accepted Answer

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

Question 4

If the point   is on the graph of an even function, what other point must also be on the graph?

Accepted Answer

The answer of If the point   is on...

Question 5

A rectangle has perimeter   m. Express the area of the rectangle as a function   of the length l of one of its sides.

Accepted Answer

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

Question 6

Use the table to evaluate the expression   .   1 2
3
4
5
6   3
2
1
0
1
2   6
5
2
3
4
6

Accepted Answer

A) 2 
B) 6 
C) 4 
D) 5 
E) 3 
A) 2 
B) 6 
C) 4 
D) 5 
E) 3

Question 7

Use the precise definition of a limit to prove that

Accepted Answer

The answer of Use the precise definition of a limit...

Question 8

The displacement (in feet) of a certain particle moving in a straight line is given by   where t is measured in seconds. Find the average velocity over the interval   Round your answer to three decimal places.

Accepted Answer

The answer of The displacement (in feet) of a certain...

Question 9

The position of a car is given by the values in the following table.   (seconds) 0
1
2
3
4   (meters)
0
21)7
26)8
62)4
86)5
Find the average velocity for the time period beginning when   and lasting 2 seconds.

Accepted Answer

A)    ft/s 
B)    ft/s 
C) 29.85 ft/s 
D) 33.5 ft/s 
E)    ft/s 
A)    ft/s 
B)    ft/s 
C) 29.85 ft/s 
D) 33.5 ft/s 
E)    ft/s

Question 10

Find the numbers, if any, where the function   is discontinuous.

Accepted Answer

The answer of Find the numbers, if any, where the...

Question 11

For x = 5, determine whether f is continuous from the right, from the left, or neither.

Accepted Answer

The answer of For x = 5, determine whether f...

Question 12

The point   lies on the curve   . If is the point Q   , use your calculator to find the slope of the secant line PQ (correct to six decimal places) for the value

Accepted Answer

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

Question 13

Use the definition of the limit to find values of   that corresponds to   .   Round your answer to the nearest thousandth.

Accepted Answer

The answer of Use the definition of the limit to...

Question 14

Given that   , and   , evaluate the limit.

Accepted Answer

The answer of Given that   , and ...

Question 15

By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box can be made. If the cardboard is 17 in. long and 10 in. wide and the square cutaways have dimensions of x in. by x in., find a function that gives the volume of the resulting box.

Accepted Answer

The answer of By cutting away identical squares from each...

Question 16

Evaluate the limit.

Accepted Answer

The answer of Evaluate the limit.  ...

Question 17

Find the function   and its domain if   and   .

Accepted Answer

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

Question 18

If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height in meters t seconds later is given by   . Find the average velocity over the time interval   .

Accepted Answer

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

Question 19

Find the vertical asymptotes of the function.

Accepted Answer

The answer of Find the vertical asymptotes of the function....

Question 20

How would you define   in order to make f continuous at   ?

Accepted Answer

A)    
B)    
C)    
D)    
E) none of these 
A)    
B)    
C)    
D)    
E) none of these

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

The graph of the function has been compressed horizontally by a factor of 3. Find the function for the transformed graph.

Evaluate the limit, if it exists.

If the point is on the graph of an even function, what other point must also be on the graph?

A rectangle has perimeter m. Express the area of the rectangle as a function of the length l of one of its sides.

Use the table to evaluate the expression . 1 2 3 4 5 6 3 2 1 0 1 2 6 5 2 3 4 6

Use the precise definition of a limit to prove that

The displacement (in feet) of a certain particle moving in a straight line is given by where t is measured in seconds. Find the average velocity over the interval Round your answer to three decimal places.

The position of a car is given by the values in the following table. (seconds) 0 1 2 3 4 (meters) 0 21)7 26)8 62)4 86)5 Find the average velocity for the time period beginning when and lasting 2 seconds.

Find the numbers, if any, where the function is discontinuous.

For x = 5, determine whether f is continuous from the right, from the left, or neither.

The point lies on the curve . If is the point Q , use your calculator to find the slope of the secant line PQ (correct to six decimal places) for the value

Use the definition of the limit to find values of that corresponds to . Round your answer to the nearest thousandth.

Given that , and , evaluate the limit.

Evaluate the limit.

Find the function and its domain if and .

If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height in meters t seconds later is given by . Find the average velocity over the time interval .

Find the vertical asymptotes of the function.

How would you define in order to make f continuous at ?

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

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Exam 1: Functions and Limits

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

The graph of the function has been compressed horizontally by a factor of 3. Find the function for the transformed graph.

Evaluate the limit, if it exists.

If the point is on the graph of an even function, what other point must also be on the graph?

A rectangle has perimeter m. Express the area of the rectangle as a function of the length l of one of its sides.

Use the table to evaluate the expression . 1 2 3 4 5 6 3 2 1 0 1 2 6 5 2 3 4 6

Use the precise definition of a limit to prove that

The displacement (in feet) of a certain particle moving in a straight line is given by where t is measured in seconds. Find the average velocity over the interval Round your answer to three decimal places.

The position of a car is given by the values in the following table. (seconds) 0 1 2 3 4 (meters) 0 21)7 26)8 62)4 86)5 Find the average velocity for the time period beginning when and lasting 2 seconds.

Find the numbers, if any, where the function is discontinuous.

For x = 5, determine whether f is continuous from the right, from the left, or neither.

The point lies on the curve . If is the point Q , use your calculator to find the slope of the secant line PQ (correct to six decimal places) for the value

Use the definition of the limit to find values of that corresponds to . Round your answer to the nearest thousandth.

Given that , and , evaluate the limit.

Evaluate the limit.

Find the function and its domain if and .

If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height in meters t seconds later is given by . Find the average velocity over the time interval .

Find the vertical asymptotes of the function.

How would you define in order to make f continuous at ?

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters