Question 1

Find the limit   , if it exists.

Accepted Answer

A)    
B) Does not exist 
C)    
D)    
A)    
B) Does not exist 
C)    
D)

Question 2

Many physical quantities are connected by inverse square laws, that is, by power functions of the form   . In particular, the illumination of an object by a light source is inversely proportional to the square of the distance from the source. Suppose that after dark you are in a room with just one lamp and you are trying to read a book. The light is too dim and so you move   the distance to the lamp. How much brighter is the light?

Accepted Answer

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

Question 3

Find the domain and sketch the graph of the function. What is its range?

Accepted Answer

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

Question 4

Find the function   ,   ,   and its domain if   ,   and   ,   .

Accepted Answer

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

Question 5

Find the limit   .

Accepted Answer

A) 5 
B)    
C)    
D)    
A) 5 
B)    
C)    
D)

Question 6

Find the limit   .

Accepted Answer

A) -2 
B) 2 
C) -4 
D) 4 
A) -2 
B) 2 
C) -4 
D) 4

Question 7

Classify the function as a Polynomial function, a Trigonometric function, an algebraic function, or other.

Accepted Answer

A) Other 
B) Trigonometric 
C) Algebraic 
D) Polynomial 
A) Other 
B) Trigonometric 
C) Algebraic 
D) Polynomial

Question 8

By graphing the function   and zooming in toward the point where the graph crosses the y-axis, estimate the value of

Accepted Answer

The answer of By graphing the function   and...

Question 9

Find the domain of the function.   =

Accepted Answer

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

Question 10

Find the value of the limit.

Accepted Answer

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

Question 11

Consider the following function.   Determine the values of a for which   exists.

Accepted Answer

The answer of Consider the following function.   Determine...

Question 12

Complete the table by computing   at the given values of x, accurate to five decimal places. Use the results to guess at the indicated limit, if it exists, to three decimal places.

Accepted Answer

The answer of Complete the table by computing  ...

Question 13

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

Accepted Answer

A)    m/s 
B)    m/s 
C)    m/s 
D)    m/s 
E)    m/s 
A)    m/s 
B)    m/s 
C)    m/s 
D)    m/s 
E)    m/s

Question 14

A machinist is required to manufacture a circular metal disk with area 1000   . If the machinist is allowed an error tolerance of   in the area of the disk, how close to the ideal radius must the machinist control the radius? Round your answer to the nearest hundred thousandth.

Accepted Answer

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

Question 15

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations.

Accepted Answer

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

Question 16

Use continuity to evaluate the limit.

Accepted Answer

The answer of Use continuity to evaluate the limit. ...

Question 17

If f and g are continuous functions with

Accepted Answer

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

Find the limit , if it exists.

Find the domain and sketch the graph of the function. What is its range?

Find the function , , and its domain if , and , .

Find the limit .

Find the limit .

Classify the function as a Polynomial function, a Trigonometric function, an algebraic function, or other.

By graphing the function and zooming in toward the point where the graph crosses the y-axis, estimate the value of

Find the domain of the function. =

Find the value of the limit.

Consider the following function. Determine the values of a for which exists.

Complete the table by computing at the given values of x, accurate to five decimal places. Use the results to guess at the indicated limit, if it exists, to three decimal places.

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

A machinist is required to manufacture a circular metal disk with area 1000 . If the machinist is allowed an error tolerance of in the area of the disk, how close to the ideal radius must the machinist control the radius? Round your answer to the nearest hundred thousandth.

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations.

Use continuity to evaluate the limit.

If f and g are continuous functions with

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

Find the limit , if it exists.

Find the domain and sketch the graph of the function. What is its range?

Find the function , , and its domain if , and , .

Find the limit .

Find the limit .

Classify the function as a Polynomial function, a Trigonometric function, an algebraic function, or other.

By graphing the function and zooming in toward the point where the graph crosses the y-axis, estimate the value of

Find the domain of the function. =

Find the value of the limit.

Consider the following function. Determine the values of a for which exists.

Complete the table by computing at the given values of x, accurate to five decimal places. Use the results to guess at the indicated limit, if it exists, to three decimal places.

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

A machinist is required to manufacture a circular metal disk with area 1000 . If the machinist is allowed an error tolerance of in the area of the disk, how close to the ideal radius must the machinist control the radius? Round your answer to the nearest hundred thousandth.

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations.

Use continuity to evaluate the limit.

If f and g are continuous functions with

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