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.

mc001-1.jpg
A
6 + C
B
6x + C
C
6x
D
6
 

 2. 

Find the indefinite integral.

mc002-1.jpg
A
mc002-2.jpg
B
mc002-3.jpg
C
mc002-4.jpg
D
mc002-5.jpg
 

 3. 

Find the indefinite integral.

mc003-1.jpg
A
mc003-2.jpg
B
mc003-3.jpg
C
mc003-4.jpg
D
mc003-5.jpg
 

 4. 

Find the indefinite integral.

mc004-1.jpg
A
mc004-2.jpg
B
mc004-3.jpg
C
mc004-4.jpg
D
mc004-5.jpg
 

 5. 

Find the indefinite integral.

mc005-1.jpg

Hint
: mc005-2.jpg
A
mc005-3.jpg
B
mc005-4.jpg
C
mc005-5.jpg
D
mc005-6.jpg
 

 6. 

Find the indefinite integral.

mc006-1.jpg
A
mc006-2.jpg
B
mc006-3.jpg
C
mc006-4.jpg
D
mc006-5.jpg
 

 7. 

Find the indefinite integral.

mc007-1.jpg
A
mc007-2.jpg
B
mc007-3.jpg
C
mc007-4.jpg
D
mc007-5.jpg
E
mc007-6.jpg
 

 8. 

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

mc008-1.jpg
A
mc008-2.jpg
B
mc008-3.jpg
C
mc008-4.jpg
D
mc008-5.jpg
 

 9. 

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

mc009-1.jpg
A
mc009-2.jpg
B
mc009-3.jpg
C
mc009-4.jpg
D
mc009-5.jpg
 

 10. 

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

mc010-1.jpg

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

mc011-1.jpg

mc011-2.jpg, where mc011-3.jpg is measured in hours, with mc011-4.jpg corresponding to 6 a.m. The temperature at 6 a.m. was mc011-5.jpg. What was the temperature at 9 a.m.? Please round your answer to whole degrees.
A
mc011-6.jpg
B
mc011-7.jpg
C
mc011-8.jpg
D
mc011-9.jpg
E
mc011-10.jpg
 

 12. 

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

mc012-1.jpg

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

Hint
: mc012-2.jpg
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.

mc013-1.jpg
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
mc014-1.jpg
8 sq units;
C
mc014-3.jpg
10 sq units;
B
mc014-2.jpg
8 sq units;
D
mc014-4.jpg
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 mc016-1.jpg and compute the Riemann sum of f over the interval mc016-2.jpg, choosing the representative points to be the midpoints of the subintervals, using five subintervals of equal length (mc016-3.jpg).
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 mc017-1.jpg 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.

mc018-1.jpg
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

mc019-1.jpg

on the interval mc019-2.jpg, using the fundamental theorem of calculus. Then verify your result using geometry.
A
mc019-3.jpg
B
mc019-4.jpg
C
mc019-5.jpg
D
mc019-6.jpg
 

 20. 

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

mc020-1.jpg

on the interval mc020-2.jpg.
A
mc020-3.jpg
B
mc020-4.jpg
C
mc020-5.jpg
D
mc020-6.jpg
 

 21. 

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

mc021-1.jpg

on the interval mc021-2.jpg.
A
mc021-3.jpg
B
mc021-4.jpg
C
mc021-5.jpg
D
mc021-6.jpg
 

 22. 

Evaluate the definite integral.

mc022-1.jpg
A
mc022-2.jpg
B
mc022-3.jpg
C
mc022-4.jpg
D
mc022-5.jpg
 

 23. 

Evaluate the definite integral.

mc023-1.jpg
A
mc023-2.jpg
B
mc023-3.jpg
C
mc023-4.jpg
D
mc023-5.jpg
E
mc023-6.jpg
 

 24. 

Find the area of the shaded region.

mc024-1.jpg
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.

mc025-1.jpg
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.

mc026-1.jpg
A
mc026-2.jpg
mc026-3.jpg
C
mc026-6.jpg
mc026-7.jpg
B
mc026-4.jpg
mc026-5.jpg
D
mc026-8.jpg
mc026-9.jpg
 

 27. 

Find the area of the region enclosed by these graphs and the vertical lines mc027-1.jpg and mc027-2.jpg.

mc027-3.jpg
A
mc027-4.jpg
B
mc027-5.jpg
C
mc027-6.jpg
D
12
E
mc027-7.jpg
 

 28. 

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

mc028-1.jpg
A
mc028-2.jpg
mc028-3.jpg
C
mc028-6.jpg
mc028-7.jpg
B
mc028-4.jpg
mc028-5.jpg
D
mc028-8.jpg
mc028-9.jpg
 

 29. 

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

mc029-1.jpg

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

mc030-1.jpg

The supply function for the compact discs of is given by

mc030-2.jpg

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

mc031-1.jpg

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

mc031-2.jpg

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 mc032-1.jpg. 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

nr033-1.jpg

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

nr034-1.jpg

The supply function for the compact discs is given by

nr034-2.jpg

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.

$__________

 

Short Answer
 

 35. 

Find the indefinite integral.

sa035-1.jpg
 

 36. 

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

sa036-1.jpg
 

 37. 

Let sa037-1.jpg and compute the Riemann sum of f over the interval sa037-2.jpg, choosing the representative points to be the midpoints of the subintervals, using:

Two subintervals of equal length (sa037-3.jpg).

__________ sq units

Five subintervals of equal length (sa037-4.jpg).

__________ sq units

Ten subintervals of equal length (sa037-5.jpg).

__________ sq units

Can you guess at the area of the region under the graph of f on the interval sa037-6.jpg?

sa037-7.jpg __________sq units
 

 38. 

The quantity demanded sa038-1.jpg (in units of a hundred) of the miniature cameras per week is related to the unit price sa038-2.jpg (in dollars) by

sa038-3.jpg

and the quantity sa038-4.jpg (in units of a hundred) that the supplier is willing to make available in the market is related to the unit price sa038-5.jpg (in dollars) by

sa038-6.jpg

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 es039-1.jpg and es039-2.jpg and the vertical lines x = 0 and x = 4 is given by es039-3.jpg
 



 
Check Your Work     Start Over