Exam 3 Review
Zarestky’s Math 142, Spring 2011
Sections 5.5, 5.6, 6.1, 6.2, 6.4, 6.5, 7.1, and 7.2
These problems are meant to be a highlight of the material covered on the exam and not a comprehensive
review! Every type of problem will not be on this review, and you should work lots of other problems
from the text and Mrs. Drosts’ reviews.
1.
Find the absolute maximum and minimum values, if either exists, for the function
1
f ( x) =
over the indicated intervals.
2
( x !5)
A. !"#0,4$&%
B. !#"0,10$&%
2.
You have 100 feet of fencing with which to fence in three sides of a rectangular pasture. A
straight river will form the fourth side. What is the largest area you can enclose?
3.
A 2000-room hotel in Las Vegas is filled to capacity every night at a rate of $400 per room. For
each $1 increase in the nightly rate, 4 fewer rooms are occupied. If each occupied room costs
$16 per day to clean and service, how much should the hotel charge per room to maximize gross
profit? What is the maximum gross profit?
4.
The marginal average cost of producing x digital sports watches is given by
1000
C !( x ) = " 2 where C ( x ) is the average cost in dollars, and C (100) = 25 . Find the average
x
cost function and the cost function. What are the fixed costs?
5.
Calculate each indefinite integral.
A.
"
C.
!
6
x 3 ! dx
x
2
3x
dx
x 3 +1
4
x 3 +1
dx
3x 2
B.
!
D.
! (x
2
+1) e x +3x dx
3
6.
Graphed below is marginal profit (in thousands of dollars per hundreds of items). Using both the
left- and right-hand rule with n = 4 equal subintervals, estimate the profit generated from
increasing production from 0 to 800 items.
7.
Given
0
"e
!3x
dx = 5 , solve for a.
a
8.
Suppose oil is being extracted from a field at a rate given by B!(t ) = 0.2e0.1t , where B(t) is
measured in millions of barrels and t is measured in years.
A. At this rate, how much oil will be extracted during the second 10-year period?
B. During the second 10-year period, what is the average yield per year?
9.
Find the indicated area.
2
on "$#!1,1%&'
x +1
B. The area bounded by y1 = x 2 !6x and y2 = x
A. The area bounded by y1 = e!x and y2 =
10.
2
Given a price-demand equation p = D ( x ) = 80 !0.04x , find consumers’ surplus when demand is
600 items.