Question 1

A family of functions is given below. Find the function f (x) such that the family is given by   . Round your answer to one decimal place, if necessary. ​   ​

Accepted Answer

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Question 2

Evaluate the integral   . ​

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Question 3

If   , find   . ​

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Question 4

Evaluate the integral   . ​

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Question 5

The rate of production of a new line of products is given by   , where x is the number of items produced and t is the number of weeks the product has been in production. Assuming that   when   , find the total number of items produced as a function of time t. ​

Accepted Answer

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Question 6

Evaluate the integral   . ​

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Question 7

Find the general solution to the differential equation   . ​

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Question 8

Suppose that a liquid carries a drug into a 500-cc organ at a rate of 15 cc/s and leaves the organ at the same rate. Suppose that the concentration of the drug entering is 0.2 g/cc. Find the amount A of drug in the organ as a function of time t if initially there is none in the organ. If it's necessary, round your calculations to four decimal places. ​

Accepted Answer

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Question 9

Find the particular solution. ​     ​

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Question 10

Evaluate the integral   . ​

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Question 11

Given the functions below, decide which function is f (x), and which is a member of the family   . ​   ​

Accepted Answer

A)    and   is a member of the family of   
B)    and   is a member of the family of   
C)    and   is a member of the family of   
D)    and   is a member of the family of   
E)    and   is a member of the family of   
A)    and   is a member of the family of   
B)    and   is a member of the family of   
C)    and   is a member of the family of   
D)    and   is a member of the family of   
E)    and   is a member of the family of

Question 12

Find the general solution to the differential equation   . ​

Accepted Answer

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Question 13

Because of job outsourcing, a western Pennsylvania town predicts that its public school population will decrease at the rate   , where x is the number of years and N is the total school population. If N = 7,800 when x = 0, what population size is expected in 6 years? Round your answer to nearest integer when applicable. ​

Accepted Answer

A)  6,376 students 
B)  7,538 students 
C)  8,438 students 
D)  7,276 students 
E)  9,600 students 
A)  6,376 students 
B)  7,538 students 
C)  8,438 students 
D)  7,276 students 
E)  9,600 students

Question 14

Find the particular solution. ​   ​

Accepted Answer

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Question 15

Suppose that a particle has been shot into the air in such a way that the rate at which its height H (in feet per second) is changing is   . If the particle is 3,100 feet high when   seconds, write the formula for the height of the particle at any time t.

Accepted Answer

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B)    
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D)    
E)    
A)    
B)    
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Question 16

If $P is invested for n years at 6% compounded continuously, the rate at which the future value is growing is   . In how many years will the future value double? Round your answer to one decimal place. ​

Accepted Answer

A)  18.3 years 
B)  13.6 years 
C)  11.6 years 
D)  20.3 years 
E)  16.6 years 
A)  18.3 years 
B)  13.6 years 
C)  11.6 years 
D)  20.3 years 
E)  16.6 years

Question 17

If   , find   . ​

Accepted Answer

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B)    
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E)

Question 18

The average cost of a product, in dollars, changes at the rate   and the average cost of 12 units is $25.00. Find the average cost of 24 units. Round your answer to the nearest cent. ​

Accepted Answer

A)  $600.00 
B)  $25.50 
C)  $50.00 
D)  $30.60 
E)  $1.50 
A)  $600.00 
B)  $25.50 
C)  $50.00 
D)  $30.60 
E)  $1.50

Question 19

A family of functions is given and the graph of some members of the family are shown. Write the indefinite integral that gives the family. ​   ​   ​

Accepted Answer

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

Question 20

Suppose an oil tanker hits a reef and begins to leak. The efforts of the workers repairing the leak cause the rate at which the oil is leaking to decrease. The oil was leaking at a rate of 39 barrels per hour at the end of the first hour after the accident, and the rate is decreasing at a rate of one barrel per hour. How many barrels of oil will leak in the first 6 hours? ​

Accepted Answer

A)  216 barrels 
B)  132 barrels 
C)  222 barrels 
D)  231 barrels 
E)  225 barrels 
A)  216 barrels 
B)  132 barrels 
C)  222 barrels 
D)  231 barrels 
E)  225 barrels

A family of functions is given below. Find the function f (x) such that the family is given by . Round your answer to one decimal place, if necessary.

Evaluate the integral .

If , find .

Evaluate the integral .

The rate of production of a new line of products is given by , where x is the number of items produced and t is the number of weeks the product has been in production. Assuming that when , find the total number of items produced as a function of time t.

Evaluate the integral .

Find the general solution to the differential equation .

Find the particular solution.

Evaluate the integral .

Given the functions below, decide which function is f (x), and which is a member of the family .

Find the general solution to the differential equation .

Find the particular solution.

Suppose that a particle has been shot into the air in such a way that the rate at which its height H (in feet per second) is changing is . If the particle is 3,100 feet high when seconds, write the formula for the height of the particle at any time t.

If $P is invested for n years at 6% compounded continuously, the rate at which the future value is growing is . In how many years will the future value double? Round your answer to one decimal place.

If , find .

The average cost of a product, in dollars, changes at the rate and the average cost of 12 units is $25.00. Find the average cost of 24 units. Round your answer to the nearest cent.

A family of functions is given and the graph of some members of the family are shown. Write the indefinite integral that gives the family.

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

Derivatives

Derivatives Continued

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

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Exam 12: Indefinite Integrals

A family of functions is given below. Find the function f (x) such that the family is given by . Round your answer to one decimal place, if necessary. ​ ​

Evaluate the integral . ​

If , find . ​

Evaluate the integral . ​

The rate of production of a new line of products is given by , where x is the number of items produced and t is the number of weeks the product has been in production. Assuming that when , find the total number of items produced as a function of time t. ​

Evaluate the integral . ​

Find the general solution to the differential equation . ​

Find the particular solution. ​ ​

Evaluate the integral . ​

Given the functions below, decide which function is f (x), and which is a member of the family . ​ ​

Find the general solution to the differential equation . ​

Find the particular solution. ​ ​

Suppose that a particle has been shot into the air in such a way that the rate at which its height H (in feet per second) is changing is . If the particle is 3,100 feet high when seconds, write the formula for the height of the particle at any time t.

If $P is invested for n years at 6% compounded continuously, the rate at which the future value is growing is . In how many years will the future value double? Round your answer to one decimal place. ​

If , find . ​

The average cost of a product, in dollars, changes at the rate and the average cost of 12 units is $25.00. Find the average cost of 24 units. Round your answer to the nearest cent. ​

A family of functions is given and the graph of some members of the family are shown. Write the indefinite integral that gives the family. ​ ​ ​

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

Derivatives

Derivatives Continued

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

A family of functions is given below. Find the function f (x) such that the family is given by . Round your answer to one decimal place, if necessary.

Evaluate the integral .

If , find .

Evaluate the integral .

The rate of production of a new line of products is given by , where x is the number of items produced and t is the number of weeks the product has been in production. Assuming that when , find the total number of items produced as a function of time t.

Evaluate the integral .

Find the general solution to the differential equation .

Find the particular solution.

Evaluate the integral .

Given the functions below, decide which function is f (x), and which is a member of the family .

Find the general solution to the differential equation .

Find the particular solution.

If $P is invested for n years at 6% compounded continuously, the rate at which the future value is growing is . In how many years will the future value double? Round your answer to one decimal place.

If , find .

The average cost of a product, in dollars, changes at the rate and the average cost of 12 units is $25.00. Find the average cost of 24 units. Round your answer to the nearest cent.

A family of functions is given and the graph of some members of the family are shown. Write the indefinite integral that gives the family.