Question 1

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

Accepted Answer

A) 4, 5, and 6 
B) 4 and 5 
C) 0 and 6 
D) 0 
E) 6 
A) 4, 5, and 6 
B) 4 and 5 
C) 0 and 6 
D) 0 
E) 6

Question 2

The oxygen consumption (in milliliter/pound/minute) for a person walking at x mph is approximated by the function   where the oxygen consumption for a runner at x mph is approximated by the function   At what speed is the oxygen consumption the same for a walker as it is for a runner? What is the level of oxygen consumption at that speed?

Accepted Answer

A) 3.1 mph, 99.6 mL/lb/min 
B) 7.1 mph, 89.6 mL/lb/min 
C) 7.6 mph, 94.6 mL/lb/min 
D) 4.6 mph, 64.6 mL/lb/min 
E) 5.6 mph, 74.6 mL/lb/min 
A) 3.1 mph, 99.6 mL/lb/min 
B) 7.1 mph, 89.6 mL/lb/min 
C) 7.6 mph, 94.6 mL/lb/min 
D) 4.6 mph, 64.6 mL/lb/min 
E) 5.6 mph, 74.6 mL/lb/min

Question 3

Assume that the demand function for a certain commodity has the form   where x is the quantity demanded, measured in units of a thousand, and p is the unit price in dollars.Suppose the quantity demanded is 4,000 (x = 4) when the unit price is $8.00 and 8,000 (x = 8) when the unit price is $4.00.Determine the demand equation.

Accepted Answer

The answer of Assume that the demand function for a...

Question 4

Use the method of bisection to find the root of the equation   , accurate to two decimal places.

Accepted Answer

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

Question 5

Find the rules for the composite functions   and

Accepted Answer

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

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 range of the function.

Accepted Answer

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

Question 8

The gross domestic product (GDP) of a certain country is projected to be   billion dollars t yr from now.
What will be the rate of change of the country's GDP 3 yr from now?
$ __________ billion/yr
What will be the rate of change of the country's GDP 5 yr from now?
$ __________ billion/yr

Accepted Answer

The answer of The gross domestic product (GDP) of a...

Question 9

Refer to the graph of the function f and determine whether the statement below is true or false.

Accepted Answer

A) True 
 B)False

Question 10

Let   Find the value of k that will make f continuous on   .   __________

Accepted Answer

The answer of Let   Find the value of...

Question 11

Let   Find the equation of the tangent line to the curve at the point   .

Accepted Answer

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

Question 12

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

Accepted Answer

The answer of Determine all values of x at which...

Question 13

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

Accepted Answer

A) x 4.9 4.99 4.999 5.001 5.01 5.1 f(x) 400 40,000 4,000,000 4,000,000 40,000 400
  
B) x 4.9 4.99 4.999 5.001 5.01 5.1 f(x) 0.0025 0.000025 0 0 0.000025 0.0025
  
C) x 4.9 4.99 4.999 5.001 5.01 5.1 f(x) 0.025 0.000025 0.000003 0.000003 0.0025 0.025
  
D) x 4.9 4.99 4.999 5.001 5.01 5.1 f(x) 400 40,000 4,000,000 4,000,000 40,000 400
The limit does not exist. 
A) x 4.9 4.99 4.999 5.001 5.01 5.1 f(x) 400 40,000 4,000,000 4,000,000 40,000 400
  
B) x 4.9 4.99 4.999 5.001 5.01 5.1 f(x) 0.0025 0.000025 0 0 0.000025 0.0025
  
C) x 4.9 4.99 4.999 5.001 5.01 5.1 f(x) 0.025 0.000025 0.000003 0.000003 0.0025 0.025
  
D) x 4.9 4.99 4.999 5.001 5.01 5.1 f(x) 400 40,000 4,000,000 4,000,000 40,000 400
The limit does not exist.

Question 14

Use the four-step process to find the slope of the tangent line to the graph of the given function at any point.

Accepted Answer

A)  6 
B)  0 
C)    
D)    
A)  6 
B)  0 
C)    
D)

Question 15

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

The answer of The following graph shows the ratio of...

Question 16

Find the rules for the composite functions   and

Accepted Answer

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

Question 17

The total worldwide box-office receipts for a long-running blockbuster movie are approximated by the function   where   is measured in millions of dollars and   is the number of months since the movie's release.What are the total box-office receipts after the first month? The second month? The third month? What will the movie gross in the long run (when   is very large)?

Accepted Answer

A) After the 1st month: $150 million; after the 2nd month: $103.8 million; after the 3rd month: $75 million; in the long run: $30 million. 
B) After the 1st month: $37.5 million; after the 2nd month: $103.8 million; after the 3rd month: $75 million; in the long run: $30 million. 
C) After the 1st month: $30 million; after the 2nd month: $75 million; after the 3rd month: $103.8 million; in the long run: $150 million. 
D) After the 1st month: $30 million; after the 2nd month: $75 million; after the 3rd month: $103.8 million; in the long run: $37.5 million. 
E) After the 1st month: $30 million; after the 2nd month: $75 million; after the 3rd month: $103.7 million; in the long run: $150 million. 
A) After the 1st month: $150 million; after the 2nd month: $103.8 million; after the 3rd month: $75 million; in the long run: $30 million. 
B) After the 1st month: $37.5 million; after the 2nd month: $103.8 million; after the 3rd month: $75 million; in the long run: $30 million. 
C) After the 1st month: $30 million; after the 2nd month: $75 million; after the 3rd month: $103.8 million; in the long run: $150 million. 
D) After the 1st month: $30 million; after the 2nd month: $75 million; after the 3rd month: $103.8 million; in the long run: $37.5 million. 
E) After the 1st month: $30 million; after the 2nd month: $75 million; after the 3rd month: $103.7 million; in the long run: $150 million.

Question 18

Let   ,   .Find the rule for the function

Accepted Answer

The answer of Let   ,   .Find...

Question 19

Find   and   , where     __________   __________

Accepted Answer

The answer of Find   and   ,...

Question 20

Find the constants m and b in the linear function f (x) = mx + b, so that f (0) = 8 and f (1) = 4.

Accepted Answer

A) m = 1 and b = 1 
B) m = 8 and b = -4 
C) m = -4 and b = 8 
D) m = 1 and b = 8 
E) m = 1 and b = -4 
A) m = 1 and b = 1 
B) m = 8 and b = -4 
C) m = -4 and b = 8 
D) m = 1 and b = 8 
E) m = 1 and b = -4

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

Use the method of bisection to find the root of the equation , accurate to two decimal places.

Find the rules for the composite functions and

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 range of the function.

The gross domestic product (GDP) of a certain country is projected to be billion dollars t yr from now. What will be the rate of change of the country's GDP 3 yr from now? $ billion/yr What will be the rate of change of the country's GDP 5 yr from now? $ billion/yr

Refer to the graph of the function f and determine whether the statement below is true or false.

Let Find the value of k that will make f continuous on . __________

Let Find the equation of the tangent line to the curve at the point .

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

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

Use the four-step process to find the slope of the tangent line to the graph of the given function at any point.

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 the rules for the composite functions and

Let , .Find the rule for the function

Find and , where

Find the constants m and b in the linear function f (x) = mx + b, so that f (0) = 8 and f (1) = 4.

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.

Use the method of bisection to find the root of the equation , accurate to two decimal places.

Find the rules for the composite functions and

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 range of the function.

The gross domestic product (GDP) of a certain country is projected to be billion dollars t yr from now. What will be the rate of change of the country's GDP 3 yr from now? $ __________ billion/yr What will be the rate of change of the country's GDP 5 yr from now? $ __________ billion/yr

Refer to the graph of the function f and determine whether the statement below is true or false.

Let Find the value of k that will make f continuous on . __________

Let Find the equation of the tangent line to the curve at the point .

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

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

Use the four-step process to find the slope of the tangent line to the graph of the given function at any point.

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 the rules for the composite functions and

Let , .Find the rule for the function

Find and , where __________ __________

Find the constants m and b in the linear function f (x) = mx + b, so that f (0) = 8 and f (1) = 4.

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

The gross domestic product (GDP) of a certain country is projected to be billion dollars t yr from now. What will be the rate of change of the country's GDP 3 yr from now? $ billion/yr What will be the rate of change of the country's GDP 5 yr from now? $ billion/yr

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 and , where