304)
Find the indefinite integral 3 3x2+ 5 5x3dx.
304)
305)
Find the indefinite integral x2e+exdx.
305)
306)
The marginal revenue for a product is given by dr
dx =
–x
(x2+12)2+ 998. Find r.
306)
307)
Use differentials to approximate 35.
307)
308)
The marginal cost function for a manufacturer’s product is dc
dq = 0.0003 q2– 0.03q+ 4,
where c is in dollars. If fixed costs are $5000, determine: (a) the manufacturer’s total cost
function; (b) the manufacturer’s average cost function.
308)
309)
The function f(x) =k(2x–x2) where k is a constant and 0 x 2, is a density function if
2
0
f(x) dx = 1. Find k so that this condition is met.
309)
310)
A bacteria population is increasing at a rate of dp
dt = 2e2t5e2t. Find p as a function of t.
310)
56
311)
Determine 37x–4dx
311)
312)
The supply equation for a certain radio is given by p= 0.5 x+ 12 where p is the price in
dollars and x is the number of radios supplied. Use differentials to approximate the price
when 1604 radios are supplied. (Hint: Use x = 1600.)
312)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
313)
A surveyor measured the length of a piece of land at 100–ft intervals (x), as shown in the table. Use
Simpson’s Rule to estimate the area of the piece of land in square feet.
xLength (ft)
050
100 60
200 80
300 55
400 50
313)
24,000 ft2
B)
24,500 ft2
25,000 ft2
29,500 ft2
314)
Suppose that the accompanying table shows the velocity of a car every second for 8 seconds. Use
the Trapezoidal Rule to approximate the distance traveled by the car in the 8 seconds.
Time (sec) Velocity (ft/sec)
016
117
218
320
419
521
618
716
817
314)
162 feet
B)
291 feet
145.5 feet
221.5 feet
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7
60
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