MATH 142 Business Math II, Week In Review
Spring, 2015, Problem Set 8 (6.1, 6.2, 6.3)
JoungDong Kim
1. Find the antiderivative.
Z
(a)
x0.01 dx
(b)
Z
5 dx
(c)
Z
1
dy
2y 5
(d)
Z
y2
√ dy
2
3
1
(e)
Z √
5
(f)
Z
u3 du
(3u2 + 4u3) du
Z √
(g) ( 2u0.1 − 0.1u1.1 ) du
2
(h)
Z (i)
Z
(j)
Z (k)
Z
3
− 6t2
t2
dt
√
√
3
( t − t5 ) dt
1
π+
x
dx
t4 + 3
dt
t2
3
(l)
Z
√
(m)
Z (n)
Z
t(t + 1) dt
1
e −
x
x
dx
e−x + 1
dx
e−x
4
2. Find the cost function for an adhesive tape manufacturer if the marginal cost, in dollars, is given
by 150 − 0.01ex , where x is the number of cases of tape produced. Assume that C(0) = 100.
3. Find the cost function for a spark plug manufacturer if the marginal cost, in dollars, is given by
30x − 4ex , where x is the number of thousands of plugs sold. Assume no fixed costs.
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4. Find the indefinite integral.
Z
(a)
8(3 − 2x)5 dx
(b)
Z
10x(2x2 + 1)3 dx
(c)
Z
(x3 + 2)(x4 + 8x + 3) 3 dx
1
6
(d)
Z
√
5
(e)
Z
ln 2x
dx
x
(f)
Z
e1/x
dx
x3
x
dx
2x2 + 5
2
7
(g)
Z
e2x − e−2x
dx
e2x + e−2x
(h)
Z
1
√ dx
x ln x
8
5. Find the revenue function for a hand purse manufacturer if the marginal revenue, in dollars, is
2
given by (1 − x)e2x−x , where x is the number of thousands of purses sold.
6. The population of a certain city for the next several years is increasing at the rate given by
2
P ′(t) = 2000(t + 10)e0.05t +t , where t is time in years measured from the beginning of 1994 when
the population was 100,000. Find the population at the end of 1995.
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√
7. An object travels with a velocity function given by v = t, where t is measured in hours and
v is measured in miles per second. What would be the difference between the upper and lower
estimates for the object if we divided the interval [0, 1] into 100 subinterval?
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