Question 1

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

Accepted Answer

A) 0 
B) -2 
C) 2 
D) ​7 
E) does not exist 
A) 0 
B) -2 
C) 2 
D) ​7 
E) does not exist

Question 2

Find the derivative at the given x-value with the numerical derivative feature of a graphing utility. ​   at   ​

Accepted Answer

A) -7.5 
B) -15 
C) -56 
D) 15 
E) 0 
A) -7.5 
B) -15 
C) -56 
D) 15 
E) 0

Question 3

Graph the function with a graphing utility and use it to predict the limit. Check your work either by using the table feature of the graphing utility or by finding the limit algebraically. ​   ​

Accepted Answer

A)    
B) 18 
C)    
D) 0 
E) does not exist 
A)    
B) 18 
C)    
D) 0 
E) does not exist

Question 4

Suppose that the cost C of removing p percent of the particulate pollution from the exhaust gases at an industrial site is given by   . Describe any discontinuities for C(p). Explain what each discontinuity means. ​

Accepted Answer

A) C(p) is discontinuous at  
) This means that not all pollution can be removed. 
B) C(p) is discontinuous at  
) This means that none of the pollution can be removed. 
C) C(p) is continuous everywhere. 
D) C(p) is discontinuous at  
) This means that not all pollution can be removed. 
E) C(p) is discontinuous at  
) This means that none of the pollution can be removed. 
A) C(p) is discontinuous at  
) This means that not all pollution can be removed. 
B) C(p) is discontinuous at  
) This means that none of the pollution can be removed. 
C) C(p) is continuous everywhere. 
D) C(p) is discontinuous at  
) This means that not all pollution can be removed. 
E) C(p) is discontinuous at  
) This means that none of the pollution can be removed.

Question 5

Differentiate the given function. ​   ​

Accepted Answer

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

Question 6

If   , find   . ​

Accepted Answer

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

Question 7

Suppose that for fiddler crabs, the allometric relationship between the weight C of the claw and the weight W of the body is given by   . Find the function that gives the rate of change of claw weight with respect to body weight. ​

Accepted Answer

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

Question 8

Find the third derivative. ​   ​

Accepted Answer

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

Question 9

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

Accepted Answer

A) 0 
B)    
C)    
D)    
E) does not exist 
A) 0 
B)    
C)    
D)    
E) does not exist

Question 10

Suppose that the demand for a product depends on the price p according to   ,   , where p is in dollars. Find and explain the meaning of the instantaneous rate of change of demand with respect to price when   . ​

Accepted Answer

A) -0.32. If price increases by $1, the demand will decrease approximately 0.32 units. 
B) 0.32. If price increases by $1, the demand will increase approximately 0.32 units. 
C) -0.64. If price increases by $1, the demand will decrease approximately 0.64 units. 
D) -49.84. If price increases by $1, the demand will increase approximately 49.84 units. 
E) 0.64. If price increases by $1, the demand will decrease approximately 0.64 units. 
A) -0.32. If price increases by $1, the demand will decrease approximately 0.32 units. 
B) 0.32. If price increases by $1, the demand will increase approximately 0.32 units. 
C) -0.64. If price increases by $1, the demand will decrease approximately 0.64 units. 
D) -49.84. If price increases by $1, the demand will increase approximately 49.84 units. 
E) 0.64. If price increases by $1, the demand will decrease approximately 0.64 units.

Question 11

Differentiate the given function. ​   ​

Accepted Answer

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

Question 12

At the indicated point, find the instantaneous rate of change of the function. ​   ​

Accepted Answer

A) 86 
B) 50 
C) 270 
D) 23 
E) 32 
A) 86 
B) 50 
C) 270 
D) 23 
E) 32

Question 13

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

Accepted Answer

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

Question 14

Determine whether the function is continuous or discontinuous at the given x-value. ​   ​

Accepted Answer

A) continuous 
B) discontinuous 
A) continuous 
B) discontinuous

Question 15

Use the numerical derivative feature of a graphing utility to find the derivative of the function at the given x-value. Round your answer to three decimal places. ​   at   ​

Accepted Answer

A) -0.437 
B) 0.875 
C) -0.292 
D) -3.062 
E) 3.062 
A) -0.437 
B) 0.875 
C) -0.292 
D) -3.062 
E) 3.062

Question 16

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

Accepted Answer

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

Question 17

The graph of a company's total cost function is shown. Does this total cost function represent a manufacturing process that is getting more efficient or less efficient as the production level increases? ​   ​

Accepted Answer

A) less efficient 
B) more efficient 
A) less efficient 
B) more efficient

Question 18

Write the equation of the line tangent to the graph of f (x) at   ​   ​

Accepted Answer

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

Question 19

A graph of   is shown and a c-value is given. For this problem, use the graph to find   . ​   ​   ​

Accepted Answer

A) 0 
B) 2 
C) -6 
D) -4 
E) does not exist 
A) 0 
B) 2 
C) -6 
D) -4 
E) does not exist

Question 20

Find all points   where the slope of the tangent is 0 for the given function. ​   ​

Accepted Answer

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

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

Find the derivative at the given x-value with the numerical derivative feature of a graphing utility. at

Graph the function with a graphing utility and use it to predict the limit. Check your work either by using the table feature of the graphing utility or by finding the limit algebraically.

Suppose that the cost C of removing p percent of the particulate pollution from the exhaust gases at an industrial site is given by . Describe any discontinuities for C(p). Explain what each discontinuity means.

Differentiate the given function.

If , find .

Suppose that for fiddler crabs, the allometric relationship between the weight C of the claw and the weight W of the body is given by . Find the function that gives the rate of change of claw weight with respect to body weight.

Find the third derivative.

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

Suppose that the demand for a product depends on the price p according to , , where p is in dollars. Find and explain the meaning of the instantaneous rate of change of demand with respect to price when .

Differentiate the given function.

At the indicated point, find the instantaneous rate of change of the function.

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

Determine whether the function is continuous or discontinuous at the given x-value.

Use the numerical derivative feature of a graphing utility to find the derivative of the function at the given x-value. Round your answer to three decimal places. at

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

The graph of a company's total cost function is shown. Does this total cost function represent a manufacturing process that is getting more efficient or less efficient as the production level increases?

Write the equation of the line tangent to the graph of f (x) at

A graph of is shown and a c-value is given. For this problem, use the graph to find .

Find all points where the slope of the tangent is 0 for the given function.

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

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

Find the derivative at the given x-value with the numerical derivative feature of a graphing utility. ​ at ​

Graph the function with a graphing utility and use it to predict the limit. Check your work either by using the table feature of the graphing utility or by finding the limit algebraically. ​ ​

Suppose that the cost C of removing p percent of the particulate pollution from the exhaust gases at an industrial site is given by . Describe any discontinuities for C(p). Explain what each discontinuity means. ​

Differentiate the given function. ​ ​

If , find . ​

Suppose that for fiddler crabs, the allometric relationship between the weight C of the claw and the weight W of the body is given by . Find the function that gives the rate of change of claw weight with respect to body weight. ​

Find the third derivative. ​ ​

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

Suppose that the demand for a product depends on the price p according to , , where p is in dollars. Find and explain the meaning of the instantaneous rate of change of demand with respect to price when . ​

Differentiate the given function. ​ ​

At the indicated point, find the instantaneous rate of change of the function. ​ ​

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

Determine whether the function is continuous or discontinuous at the given x-value. ​ ​

Use the numerical derivative feature of a graphing utility to find the derivative of the function at the given x-value. Round your answer to three decimal places. ​ at ​

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

The graph of a company's total cost function is shown. Does this total cost function represent a manufacturing process that is getting more efficient or less efficient as the production level increases? ​ ​

Write the equation of the line tangent to the graph of f (x) at ​ ​

A graph of is shown and a c-value is given. For this problem, use the graph to find . ​ ​ ​

Find all points where the slope of the tangent is 0 for the given function. ​ ​

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

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

Find the derivative at the given x-value with the numerical derivative feature of a graphing utility. at

Graph the function with a graphing utility and use it to predict the limit. Check your work either by using the table feature of the graphing utility or by finding the limit algebraically.

Suppose that the cost C of removing p percent of the particulate pollution from the exhaust gases at an industrial site is given by . Describe any discontinuities for C(p). Explain what each discontinuity means.

Differentiate the given function.

If , find .

Suppose that for fiddler crabs, the allometric relationship between the weight C of the claw and the weight W of the body is given by . Find the function that gives the rate of change of claw weight with respect to body weight.

Find the third derivative.

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

Suppose that the demand for a product depends on the price p according to , , where p is in dollars. Find and explain the meaning of the instantaneous rate of change of demand with respect to price when .

Differentiate the given function.

At the indicated point, find the instantaneous rate of change of the function.

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

Determine whether the function is continuous or discontinuous at the given x-value.

Use the numerical derivative feature of a graphing utility to find the derivative of the function at the given x-value. Round your answer to three decimal places. at

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

The graph of a company's total cost function is shown. Does this total cost function represent a manufacturing process that is getting more efficient or less efficient as the production level increases?

Write the equation of the line tangent to the graph of f (x) at

A graph of is shown and a c-value is given. For this problem, use the graph to find .

Find all points where the slope of the tangent is 0 for the given function.