Question 1

Determine all values of x at which the function is discontinuous.

Accepted Answer

A)  - 5 
B)  0, 5 
C)  0, - 5 
D)  - 3 
E)  3 
A)  - 5 
B)  0, 5 
C)  0, - 5 
D)  - 3 
E)  3 B

Question 2

Find and simplify   for the function.

Accepted Answer

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

Question 3

Let   and   . Find the rule for the function   .

Accepted Answer

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

Question 4

Find the functions f + g, f - g, fg, and

Accepted Answer

The answer of Find the functions f + g, f...

Question 5

Find the indicated limit.

Accepted Answer

The answer of Find the indicated limit.  ...

Question 6

a) Determine whether the equation defines y as a linear function of x, and b) if so, write it in the form y = mx + b.
x = 5y - 20
a) Answer yes or no. __________
b) If yes, then __________

Accepted Answer

The answer of a) Determine whether the equation defines y...

Question 7

Find the slope of the tangent line to the graph of each function at the given point and determine an equation of the tangent line.

Accepted Answer

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

Question 8

Let f be the function defined by f (x) = 4x + 8. Find f (1), f (- 1), f (a), f (- a), and f (a + 1).

Accepted Answer

A)  f (1) = 11, f (- 1) = 5, f (a) = 4a + 8, f(- a) = - 4a + 8 
B)  f (1) = 10, f (- 1) = 6, f (a) = 12, f(- a) = 4, f (a + 1) = 4a + 12 
C)  f (1) = 12, f (- 1) = 4, f (a) = a + 8, f(- a) = - a + 8, f (a + 1) = 4a + -4 
D)  f (1) = 12, f (- 1) = 4, f (a) = 4a + 8, f(- a) = - 4a + 8, f (a + 1) = 4a + 12 
E)  f (1) = 12, f (- 1) = 4, f (a) = 4a + 8, f(- a) = 4, f (a + 1) = 4a + 8 
A)  f (1) = 11, f (- 1) = 5, f (a) = 4a + 8, f(- a) = - 4a + 8 
B)  f (1) = 10, f (- 1) = 6, f (a) = 12, f(- a) = 4, f (a + 1) = 4a + 12 
C)  f (1) = 12, f (- 1) = 4, f (a) = a + 8, f(- a) = - a + 8, f (a + 1) = 4a + -4 
D)  f (1) = 12, f (- 1) = 4, f (a) = 4a + 8, f(- a) = - 4a + 8, f (a + 1) = 4a + 12 
E)  f (1) = 12, f (- 1) = 4, f (a) = 4a + 8, f(- a) = 4, f (a + 1) = 4a + 8

Question 9

Find the indicated one-sided limit.

Accepted Answer

The answer of Find the indicated one-sided limit.  ...

Question 10

Find the limit.

Accepted Answer

The answer of Find the limit.  ...

Question 11

Find the limit, if it exists.

Accepted Answer

A)    
B)    
C)    
D)  The limit does not exist 
A)    
B)    
C)    
D)  The limit does not exist

Question 12

Find the limit.

Accepted Answer

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

Question 13

Find the rules for the composite functions   and

Accepted Answer

The answer of Find the rules for the composite functions...

Question 14

Complete the table by computing   at the given values of x. Use these results to estimate   (if it exists).

Accepted Answer

A)  x 6.9 6.99 6.999 7.001 7.01 7.1 f(x) 53.91 55.7901 55.979001 56.007001 56.0701 56.71
  
B)  x 6.9 6.99 6.999 7.001 7.01 7.1 f(x) 54.61 55.8601 55.986001 56.014001 56.1401 57.41
  
C)  x 6.9 6.99 6.999 7.001 7.01 7.1 f(x) 54.41 55.8401 55.984001 56.012001 56.1201 57.21
  
D)  x 6.9 6.99 6.999 7.001 7.01 7.1 f(x) 55.01 55.9001 55.990001 56.018001 56.1801 57.81
The limit does not exist 
A)  x 6.9 6.99 6.999 7.001 7.01 7.1 f(x) 53.91 55.7901 55.979001 56.007001 56.0701 56.71
  
B)  x 6.9 6.99 6.999 7.001 7.01 7.1 f(x) 54.61 55.8601 55.986001 56.014001 56.1401 57.41
  
C)  x 6.9 6.99 6.999 7.001 7.01 7.1 f(x) 54.41 55.8401 55.984001 56.012001 56.1201 57.21
  
D)  x 6.9 6.99 6.999 7.001 7.01 7.1 f(x) 55.01 55.9001 55.990001 56.018001 56.1801 57.81
The limit does not exist

Question 15

Find f (a + h) - f (a) for the function f (x) = 8x + 5. Simplify your answer.

Accepted Answer

A)  5a + 8h 
B)  5h + 8 
C)  8a-8h 
D)  8h + 5 
E)  8h 
A)  5a + 8h 
B)  5h + 8 
C)  8a-8h 
D)  8h + 5 
E)  8h

Question 16

Select the correct graph of the function f and evaluate   if it exists.           Select the correct graph of the function. Answer A, B, C or 
D.
__________
Evaluate the limit. If the limit does not exist, answer no solution.
__________

Accepted Answer

The answer of Select the correct graph of the function...

Question 17

Refer to the graph of the function f in the following figure.   Find the value of x for which (i) f (x) = 3 and (ii) f (x) = 0.

Accepted Answer

A)  f (3) = 3, f (2) = 0 
B)  f (4) = 3, f (3) = 0 
C)  f (4) = 3, f (2) = 0 
D)  f (3) = 3, f (1) = 0 
E)  f (3) = 5, f (0) = -2 
A)  f (3) = 3, f (2) = 0 
B)  f (4) = 3, f (3) = 0 
C)  f (4) = 3, f (2) = 0 
D)  f (3) = 3, f (1) = 0 
E)  f (3) = 5, f (0) = -2

Question 18

Find the indicated one-sided limit.

Accepted Answer

A)  81 
B)  0 
C)  -18 
D)    
E)    
A)  81 
B)  0 
C)  -18 
D)    
E)

Question 19

The following graph shows the ratio of bachelor's degrees earned by women to men from 1960 through 1990. How fast was the ratio changing in the period from 1960 to 1980? From 1980 to 1990?

Accepted Answer

A)  0.0235/yr from 1960 through 1980 0.006/yr from 1980 through 1990 
B)  0.47/yr from 1960 through 1980 0.06/yr from 1980 through 1990 
C)  0.047/yr from 1960 through 1980 0.006/yr from 1980 through 1990 
D)  0.235/yr from 1960 through 1980 0.06/yr from 1980 through 1990 
E)  0.047/yr from 1960 through 1980 0.012/yr from 1980 through 1990 
A)  0.0235/yr from 1960 through 1980 0.006/yr from 1980 through 1990 
B)  0.47/yr from 1960 through 1980 0.06/yr from 1980 through 1990 
C)  0.047/yr from 1960 through 1980 0.006/yr from 1980 through 1990 
D)  0.235/yr from 1960 through 1980 0.06/yr from 1980 through 1990 
E)  0.047/yr from 1960 through 1980 0.012/yr from 1980 through 1990

Question 20

Find   given that   and   .

Accepted Answer

The answer of Find   given that  ...

Determine all values of x at which the function is discontinuous.

Find and simplify for the function.

Let and . Find the rule for the function .

Find the functions f + g, f - g, fg, and

Find the indicated limit.

a) Determine whether the equation defines y as a linear function of x, and b) if so, write it in the form y = mx + b. x = 5y - 20 a) Answer yes or no. b) If yes, then

Find the slope of the tangent line to the graph of each function at the given point and determine an equation of the tangent line.

Let f be the function defined by f (x) = 4x + 8. Find f (1), f (- 1), f (a), f (- a), and f (a + 1).

Find the indicated one-sided limit.

Find the limit.

Find the limit, if it exists.

Find the limit.

Find the rules for the composite functions and

Complete the table by computing at the given values of x. Use these results to estimate (if it exists).

Find f (a + h) - f (a) for the function f (x) = 8x + 5. Simplify your answer.

Select the correct graph of the function f and evaluate if it exists. Select the correct graph of the function. Answer A, B, C or D. Evaluate the limit. If the limit does not exist, answer no solution.

Refer to the graph of the function f in the following figure. Find the value of x for which (i) f (x) = 3 and (ii) f (x) = 0.

Find the indicated one-sided limit.

The following graph shows the ratio of bachelor's degrees earned by women to men from 1960 through 1990. How fast was the ratio changing in the period from 1960 to 1980? From 1980 to 1990?

Find given that and .

Preliminaries

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters

Exam 2: Functions, Limits and the Derivative

Determine all values of x at which the function is discontinuous.

Find and simplify for the function.

Let and . Find the rule for the function .

Find the functions f + g, f - g, fg, and

Find the indicated limit.

a) Determine whether the equation defines y as a linear function of x, and b) if so, write it in the form y = mx + b. x = 5y - 20 a) Answer yes or no. __________ b) If yes, then __________

Find the slope of the tangent line to the graph of each function at the given point and determine an equation of the tangent line.

Let f be the function defined by f (x) = 4x + 8. Find f (1), f (- 1), f (a), f (- a), and f (a + 1).

Find the indicated one-sided limit.

Find the limit.

Find the limit, if it exists.

Find the limit.

Find the rules for the composite functions and

Complete the table by computing at the given values of x. Use these results to estimate (if it exists).

Find f (a + h) - f (a) for the function f (x) = 8x + 5. Simplify your answer.

Select the correct graph of the function f and evaluate if it exists. Select the correct graph of the function. Answer A, B, C or D. __________ Evaluate the limit. If the limit does not exist, answer no solution. __________

Refer to the graph of the function f in the following figure. Find the value of x for which (i) f (x) = 3 and (ii) f (x) = 0.

Find the indicated one-sided limit.

The following graph shows the ratio of bachelor's degrees earned by women to men from 1960 through 1990. How fast was the ratio changing in the period from 1960 to 1980? From 1980 to 1990?

Find given that and .

Preliminaries

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters

a) Determine whether the equation defines y as a linear function of x, and b) if so, write it in the form y = mx + b. x = 5y - 20 a) Answer yes or no. b) If yes, then

Select the correct graph of the function f and evaluate if it exists. Select the correct graph of the function. Answer A, B, C or D. Evaluate the limit. If the limit does not exist, answer no solution.