Business: average revenue, cost, and profit. Given revenue and cost function R ( x ) = 40 x and C ( x ) = 5 x + 100 , R ( x ) find each for the following. Assume C ( x ) are in dollars and x is the number of lamps produced. [ 1 . 6 ] a. The average cost, the average revenue, and the average profit when x lamps are produced and sold b. The rate at which average cost is changing when 9 lamps are produced Average cost is dropping at approximately $ 1.33 per lamp.
Business: average revenue, cost, and profit. Given revenue and cost function R ( x ) = 40 x and C ( x ) = 5 x + 100 , R ( x ) find each for the following. Assume C ( x ) are in dollars and x is the number of lamps produced. [ 1 . 6 ] a. The average cost, the average revenue, and the average profit when x lamps are produced and sold b. The rate at which average cost is changing when 9 lamps are produced Average cost is dropping at approximately $ 1.33 per lamp.
Solution Summary: The author calculates the average cost, average revenue, and average profit when x lamps are produced and sold.
Business: average revenue, cost, and profit. Given revenue and cost function
R
(
x
)
=
40
x
and
C
(
x
)
=
5
x
+
100
,
R
(
x
)
find each for the following. Assume
C
(
x
)
are in dollars and x is the number of lamps produced.
[
1
.
6
]
a. The average cost, the average revenue, and the average profit when x lamps are produced and sold
b. The rate at which average cost is changing when 9 lamps are produced
Average cost is dropping at approximately
$
1.33
per lamp.
EXAMPLE 3
Find
S
X
√√2-2x2
dx.
SOLUTION Let u = 2 - 2x². Then du =
Χ
dx =
2- 2x²
=
信
du
dx, so x dx =
du and
u-1/2 du
(2√u) + C
+ C (in terms of x).
Let g(z) =
z-i
z+i'
(a) Evaluate g(i) and g(1).
(b) Evaluate the limits
lim g(z), and lim g(z).
2-12
(c) Find the image of the real axis under g.
(d) Find the image of the upper half plane {z: Iz > 0} under the function g.
k
(i) Evaluate
k=7
k=0
[Hint: geometric series + De Moivre]
(ii) Find an upper bound for the expression
1
+2x+2
where z lies on the circle || z|| = R with R > 10. [Hint: Use Cauchy-Schwarz]
Elementary Statistics: Picturing the World (7th Edition)
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