Name:    MAT 121 Chapter 6 Test

Multiple Choice
Identify the choice that best completes the statement or answers the question.

1.

Find the indefinite integral.

 A 6 + C B 6x + C C 6x D 6

2.

Find the indefinite integral.

 A B C D

3.

Find the indefinite integral.

 A B C D

4.

Find the indefinite integral.

 A B C D

5.

Find the indefinite integral.

Hint
:
 A B C D

6.

Find the indefinite integral.

 A B C D

7.

Find the indefinite integral.

 A B C D E

8.

Find f(x) by solving the initial value problem.

 A B C D

9.

Find f(x) by solving the initial value problem.

 A B C D

10.

Lorimar Watch Company manufactures travel clocks. The daily marginal cost function associated with producing these clocks is

where C '(x) is measured in dollars/unit and x denotes the number of units produced. Management has determined that the daily fixed cost incurred in producing these clocks is \$170. Find the total cost incurred by Lorimar in producing the first 400 travel clocks/day.
 A \$3,566 B \$3,354 C \$3,282 D \$3,485

11.

The temperature on a certain day as measured at the airport of a city is changing at the rate of

, where is measured in hours, with corresponding to 6 a.m. The temperature at 6 a.m. was . What was the temperature at 9 a.m.? Please round your answer to whole degrees.
 A B C D E

12.

The velocity, in feet/second, of a rocket t seconds into vertical flight is given by

What is the altitude of the rocket 40 seconds after liftoff?

Hint
:
 A 89,200 ft B 88,900 ft C 89,400 ft D 89,100 ft

13.

Find an approximation of the area of the region R under the graph of  f by computing the Riemann sum of  f corresponding to the partition of the interval into the subintervals shown in the accompanying figures. Use the midpoints of the subintervals as the representative points. Round your answer to the nearest hundredth.

 A 1.92 sq units B 0.85 sq units C 2.34 sq units D 2.27 sq units

14.

Let f(x) = 4x

Sketch the region R under the graph of  f on the interval [0, 2] and find its exact area using geometry.
 A 8 sq units; C 10 sq units; B 8 sq units; D 10 sq units;

15.

Let f(x) = 8x

Use a Riemann sum with four subintervals of equal length (n = 4) to approximate the area of R (under the graph of  f on the interval [0, 2]). Choose the representative points to be the left end points of the subintervals.

Repeat previous part with eight subintervals of equal length (n = 8).

Compare the approximations obtained in previous parts with the exact area (16 sq units). Do the approximations improve with larger n?
 A 12 sq units; 14 sq units; no B 12 sq units; 14 sq units; yes C 14 sq units; 12 sq units; no D 14 sq units; 12 sq units; yes

16.

Let and compute the Riemann sum of f over the interval , choosing the representative points to be the midpoints of the subintervals, using five subintervals of equal length ().
 A 12.3325 sq units B 15 sq units C 12.33 sq units D 11 sq units E 12.3125 sq units

17.

Let and compute the Riemann sum of f over the interval [2, 4] , using

Two subintervals of equal length (n = 2).

Five subintervals of equal length (n = 5).

Ten subintervals of equal length (n = 10).

In each case, choose the representative points to be the right end points of the subintervals.
 A 100 sq units; 84.48 sq units; 79.52 sq units; B 79.52 sq units; 84.48 sq units; 100 sq units; C 100 sq units; 79.52 sq units; 84.48 sq units; D 84.48 sq units; 79.52 sq units; 100 sq units;

18.

Find an approximation of the area of the region R under the graph of the function f on the interval [a, b]. Use n subintervals and choose the representative points as indicated.

 A 1.77 sq units; B 1.54 sq units; C 1.4 sq units; D 1.9 sq units;

19.

Find the area of the region under the graph of the function

on the interval , using the fundamental theorem of calculus. Then verify your result using geometry.
 A B C D

20.

Find the area of the region under the graph of the function

on the interval .
 A B C D

21.

Find the area of the region under the graph of the function

on the interval .
 A B C D

22.

Evaluate the definite integral.

 A B C D

23.

Evaluate the definite integral.

 A B C D E

24.

Find the area of the shaded region.

 A A = 21.3 sq units. B A = 19.9 sq units. C A = 18.1 sq units. D A = 23.6 sq units.

25.

Find the area of the shaded region.

 A A = 13 sq units. B A = 9 sq units. C A = 12 sq units. D A = 10 sq units.

26.

Sketch the graphs of the functions f and g and find the area of the region enclosed by these graphs and the vertical lines x = a and x = b.

 A C B D

27.

Find the area of the region enclosed by these graphs and the vertical lines and .

 A B C D 12 E

28.

Sketch the graph and find the area of the region completely enclosed by the graphs of the given functions f and g.

 A C B D

29.

The demand function for a certain make of replacement cartridges for a water purifier is given by

where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the consumers' surplus if the market price is set at \$5/cartridge. Round your answer to the nearest dollar.
 A \$16,886 B \$16,800 C \$16,333 D \$16,667

30.

The demand function for a certain brand of compact disc is given by

The supply function for the compact discs of is given by

where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the producers' surplus if the wholesale market price is set at the equilibrium price. Round your answer to the nearest dollar.
 A \$11,894 B \$11,792 C \$11,346 D \$11,667

31.

The management of the Titan Tire Company has determined that the quantity demanded x of their Super Titan tires/week is related to the unit price p by the relation

where p is measured in dollars and x is measured in units of a thousand. Titan will make x units of the tires available in the market if the unit price is

dollars. Determine the consumers' surplus and the producers' surplus when the market unit price is set at the equilibrium price. Round your answers to the nearest dollar.
 A CS = \$337,012 , PS = \$174,988 B CS = \$343,476 , PS = \$168,524 C CS = \$341,333 , PS = \$170,667 D CS = \$342,567 , PS = \$169,433

32.

Find . Round your answer to the nearest integer.
 A 1,619,649 B 1,607,304 C 1,622,538 D 1,562,181

Numeric Response

33.

Annual sales (in millions of units) of hand-held computers are expected to grow in accordance with the function

where t is measured in years, with t = 0 corresponding to 1997. How many hand-held computers will be sold over the 6-year period between the beginning of 1997 and the end of 2002?  Round your answer to two decimal places, if necessary.

34.

The demand function for a certain brand of compact disc is given by

The supply function for the compact discs is given by

where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the producers' surplus if the wholesale market price is set at the equilibrium price. Round your answer to the nearest dollar.

\$__________

35.

Find the indefinite integral.

36.

Find f(x) by solving the initial value problem.

37.

Let and compute the Riemann sum of f over the interval , choosing the representative points to be the midpoints of the subintervals, using:

Two subintervals of equal length ().

__________ sq units

Five subintervals of equal length ().

__________ sq units

Ten subintervals of equal length ().

__________ sq units

Can you guess at the area of the region under the graph of f on the interval ?

__________sq units

38.

The quantity demanded (in units of a hundred) of the miniature cameras per week is related to the unit price (in dollars) by

and the quantity (in units of a hundred) that the supplier is willing to make available in the market is related to the unit price (in dollars) by

If the market price is set at the equilibrium price, find the consumers' surplus and the producers' surplus. Please round the answers to the nearest dollar.

The consumers' surplus: \$__________

The producers' surplus: \$__________

Essay

39.

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.

The area of the region bounded by the graphs of and and the vertical lines x = 0 and x = 4 is given by