Question 1

Find the indefinite integral.

Accepted Answer

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

Question 2

Evaluate the integral   .

Accepted Answer

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

Question 3

Using data from the U.S. Bureau of the Census, the model   gives the projected rate of change in the number of people within one year of retirement, where t is the number of years since 1940, for the years between 1940 and 2050. Use the equation and ten midpoint rectangles to estimate, to four decimal places, the change in the population within one year of retirement or older from the end of 2037 through the end of 2042.

Accepted Answer

A)  10.0000 million retirees 
B)  7.6075 million retirees 
C)  7.5896 million retirees 
D)  7.6608 million retirees 
E)  7.6783 million retirees 
A)  10.0000 million retirees 
B)  7.6075 million retirees 
C)  7.5896 million retirees 
D)  7.6608 million retirees 
E)  7.6783 million retirees

Question 4

If possible, find the general antiderivative of   .

Accepted Answer

A)  There is no general antiderivative. 
B)    
C)    
D)    
E)    
A)  There is no general antiderivative. 
B)    
C)    
D)    
E)

Question 5

Find the indefinite integral.

Accepted Answer

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

Question 6

The function   gives the rate of change of profit for a new business during its first year. The input is the number of months since the business opened, and the output units are millions of dollars per month. What is the interpretation, in context, of the accumulation function   ?

Accepted Answer

A)    is how fast the profit, in millions of dollars, is changing at x months. 
B)    is the number of months it will take to make x millions of dollars. 
C)    is the amount of profit, in millions of dollars, the business made in month x. 
D)    is the amount of profit, in millions of dollars, the business made after month x in its first year. 
E)    is the amount of profit, in millions of dollars, the business has made in its first x months. 
A)    is how fast the profit, in millions of dollars, is changing at x months. 
B)    is the number of months it will take to make x millions of dollars. 
C)    is the amount of profit, in millions of dollars, the business made in month x. 
D)    is the amount of profit, in millions of dollars, the business made after month x in its first year. 
E)    is the amount of profit, in millions of dollars, the business has made in its first x months.

Question 7

Blood pressure varies for individuals throughout the course of a day, typically being the lowest at night and the highest from late morning to early afternoon. The estimated rate of change in diastolic blood pressure for a patient with untreated hypertension is shown in the table. Using a model for the data, estimate to one decimal place, the average rate of change in diastolic blood pressure from noon. to 8 P.M.

Accepted Answer

A)  -0.9 mm Hg per hour 
B)  -0.7 mm Hg per hour 
C)  -0.2 mm Hg per hour 
D)  -0.4 mm Hg per hour 
E)  0.3 mm Hg per hour 
A)  -0.9 mm Hg per hour 
B)  -0.7 mm Hg per hour 
C)  -0.2 mm Hg per hour 
D)  -0.4 mm Hg per hour 
E)  0.3 mm Hg per hour

Question 8

Consider the graph of the function:   Identify, from the graphs a through f, the derivative graph and the accumulation graph (with point A as the starting point). 
a:   b:   c:   d:   e:   f:

Accepted Answer

A)  The derivative is graph a and the accumulation graph is graph b. 
B)  The derivative is graph e and the accumulation graph is graph c. 
C)  The derivative is graph c and the accumulation graph is graph e. 
D)  The derivative is graph d and the accumulation graph is graph a. 
E)  The derivative is graph c and the accumulation graph is graph d. 
A)  The derivative is graph a and the accumulation graph is graph b. 
B)  The derivative is graph e and the accumulation graph is graph c. 
C)  The derivative is graph c and the accumulation graph is graph e. 
D)  The derivative is graph d and the accumulation graph is graph a. 
E)  The derivative is graph c and the accumulation graph is graph d.

Question 9

The acceleration of a race car during the first 35 seconds of a road test is modeled by   where t is the number of seconds since the test began. Assume the velocity and distance were both zero at the beginning of the road test. Calculate, to the nearest foot, the distance traveled during the first 35 seconds of the road test.

Accepted Answer

A)  708 ft 
B)  259 ft 
C)  1,552 ft 
D)  4,558 ft 
E)  9,071 ft 
A)  708 ft 
B)  259 ft 
C)  1,552 ft 
D)  4,558 ft 
E)  9,071 ft

Question 10

Consider the graph of r(t), the rate of change in the price of a technology stock, during the first 55 days of trading of 2003. Using the information present below, label each region as representing positive or negative change in price.

Accepted Answer

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

Find the indefinite integral.

Evaluate the integral .

If possible, find the general antiderivative of .

Find the indefinite integral.

The function gives the rate of change of profit for a new business during its first year. The input is the number of months since the business opened, and the output units are millions of dollars per month. What is the interpretation, in context, of the accumulation function ?

Consider the graph of the function: Identify, from the graphs a through f, the derivative graph and the accumulation graph (with point A as the starting point). a: b: c: d: e: f:

Consider the graph of r(t), the rate of change in the price of a technology stock, during the first 55 days of trading of 2003. Using the information present below, label each region as representing positive or negative change in price.

Ingredients of Change: Functions an Limits

Describing Change: Rates

Determining Change: Derivatives

Analyzing Change: Applications of Derivatives

Analyzing Accumulated Change: Integrals in Action

Ingredients of Multivariable Change: Models, Graphs, Rates

Analyzing Multivariable Change: Optimization

Filters

Exam 5: Accumulating Change: Limits of Sums and the Definite Integral

Find the indefinite integral.

Evaluate the integral .

If possible, find the general antiderivative of .

Find the indefinite integral.

The function gives the rate of change of profit for a new business during its first year. The input is the number of months since the business opened, and the output units are millions of dollars per month. What is the interpretation, in context, of the accumulation function ?

Consider the graph of the function: Identify, from the graphs a through f, the derivative graph and the accumulation graph (with point A as the starting point). a: b: c: d: e: f:

Consider the graph of r(t), the rate of change in the price of a technology stock, during the first 55 days of trading of 2003. Using the information present below, label each region as representing positive or negative change in price.

Ingredients of Change: Functions an Limits

Describing Change: Rates

Determining Change: Derivatives

Analyzing Change: Applications of Derivatives

Analyzing Accumulated Change: Integrals in Action

Ingredients of Multivariable Change: Models, Graphs, Rates

Analyzing Multivariable Change: Optimization

Filters