Question 1

Differentiate the given function. ​   ​

Accepted Answer

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

Question 2

If an IRA is a variable-rate investment for 20 years at rate r percent per year, compounded monthly, then the future value S that accumulates from an initial investment of $4,000 is   . What is the rate of change of S with respect to r and what does it tell us if the interest rate is 3%? Round your answer to two decimal places. ​

Accepted Answer

A) The future value increases by approximately $1,547.37 when the interest rate increases from 3% to 4%. 
B) The future value increases by approximately $1,452.97 when the interest rate increases from 3% to 4%. 
C) The future value increases by approximately $3,141.04 when the interest rate increases from 3% to 4%. 
D) The future value increases by approximately $1,154.17 when the interest rate increases from 3% to 4%. 
E) The future value increases by approximately $2,627.64 when the interest rate increases from 3% to 4%. 
A) The future value increases by approximately $1,547.37 when the interest rate increases from 3% to 4%. 
B) The future value increases by approximately $1,452.97 when the interest rate increases from 3% to 4%. 
C) The future value increases by approximately $3,141.04 when the interest rate increases from 3% to 4%. 
D) The future value increases by approximately $1,154.17 when the interest rate increases from 3% to 4%. 
E) The future value increases by approximately $2,627.64 when the interest rate increases from 3% to 4%.

Question 3

Find the derivative of the given function. Simplify and express the answer using positive exponents only. ​   ​

Accepted Answer

A)    
B)    
C) 30 
D) 0 
E)    
A)    
B)    
C) 30 
D) 0 
E)

Question 4

Total revenue is in dollars and x is the number of units. Suppose that the total revenue function for a commodity is   . Find   , and explain what this value represents. Round your answer to two decimal places. ​

Accepted Answer

A) $18.30 is the marginal revenue from the 71st unit. 
B) $17.60 is the marginal revenue from the 71st unit. 
C) $1,281.00 is the marginal revenue from the 71st unit. 
D) $1,298.59 is the actual revenue from the 71st unit. 
E) $17.59 is the actual revenue from the 71st unit. 
A) $18.30 is the marginal revenue from the 71st unit. 
B) $17.60 is the marginal revenue from the 71st unit. 
C) $1,281.00 is the marginal revenue from the 71st unit. 
D) $1,298.59 is the actual revenue from the 71st unit. 
E) $17.59 is the actual revenue from the 71st unit.

Question 5

Use analytic methods to evaluate the limit and determine which type of asymptote (if any) it represents. You can verify your conclusion by graphing the function with a graphing utility, if one is available. ​   ​

Accepted Answer

A) limit = 0, vertical asymptote 
B) limit = 0, horizontal asymptote 
C) limit = 2, horizontal asymptote 
D) limit = 2, vertical asymptote 
E) does not exist 
A) limit = 0, vertical asymptote 
B) limit = 0, horizontal asymptote 
C) limit = 2, horizontal asymptote 
D) limit = 2, vertical asymptote 
E) does not exist

Question 6

Suppose that the average number of minutes M that it takes a new employee to assemble one unit of a product is given by   , where t is the number of days on the job. What is the domain for this application? ​

Accepted Answer

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

Question 7

For the given function, find the slope of the tangent line at   . ​   ​

Accepted Answer

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

Question 8

Use properties of limits and algebraic methods to find   if the limit exists. ​

Accepted Answer

A) 0 
B) 10 
C) ∞ 
D) -10 
E) 5 
A) 0 
B) 10 
C) ∞ 
D) -10 
E) 5

Differentiate the given function.

Find the derivative of the given function. Simplify and express the answer using positive exponents only.

Total revenue is in dollars and x is the number of units. Suppose that the total revenue function for a commodity is . Find , and explain what this value represents. Round your answer to two decimal places.

Use analytic methods to evaluate the limit and determine which type of asymptote (if any) it represents. You can verify your conclusion by graphing the function with a graphing utility, if one is available.

Suppose that the average number of minutes M that it takes a new employee to assemble one unit of a product is given by , where t is the number of days on the job. What is the domain for this application?

For the given function, find the slope of the tangent line at .

Use properties of limits and algebraic methods to find if the limit exists.

Algebraic Concepts

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; Data Description

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Exam 10: Derivatives

Differentiate the given function. ​ ​

Find the derivative of the given function. Simplify and express the answer using positive exponents only. ​ ​

Total revenue is in dollars and x is the number of units. Suppose that the total revenue function for a commodity is . Find , and explain what this value represents. Round your answer to two decimal places. ​

Use analytic methods to evaluate the limit and determine which type of asymptote (if any) it represents. You can verify your conclusion by graphing the function with a graphing utility, if one is available. ​ ​

Suppose that the average number of minutes M that it takes a new employee to assemble one unit of a product is given by , where t is the number of days on the job. What is the domain for this application? ​

For the given function, find the slope of the tangent line at . ​ ​

Use properties of limits and algebraic methods to find if the limit exists. ​

Algebraic Concepts

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; Data Description

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Differentiate the given function.

Find the derivative of the given function. Simplify and express the answer using positive exponents only.

Total revenue is in dollars and x is the number of units. Suppose that the total revenue function for a commodity is . Find , and explain what this value represents. Round your answer to two decimal places.

Use analytic methods to evaluate the limit and determine which type of asymptote (if any) it represents. You can verify your conclusion by graphing the function with a graphing utility, if one is available.

Suppose that the average number of minutes M that it takes a new employee to assemble one unit of a product is given by , where t is the number of days on the job. What is the domain for this application?

For the given function, find the slope of the tangent line at .

Use properties of limits and algebraic methods to find if the limit exists.