MATH 142 Business Math II, Week In Review
Spring, 2015, Problem Set 10 (Exam3 Review)
JoungDong Kim
1. Evaluate
2. What is the domain of f (x, y) =
Z
√
5x2 − 2 x − 3
√
dx
6
x
p
x2 + y
.
y − 2x
1
3. Evaluate
4. If f (x, y) =
Z
ex − e−x
dx
ex + e−x
2x2 y − 4x
, what is fy ?
y2 − x
2
5. If g(x) =
Z
0
x
f (t)dt, where the graph of f (t) is given below, where 0 ≤ x ≤ 10, evaluate
g(0), g(3), g(6) and g(10).
3
6. A manufacturer has modeled its yealy production function P as a Cobb-Douglas function
P (L, K) = 1.5L0.25 K 0.75
where L is the number of labor hours and K is the invested capital. Find the marginal productivity
of capital when L = 130 and K = 30.
Z
7. Given
4
x dx = 7.5,
1
a)
Z
4
Z
5
1
b)
Z
4
2
x dx = 21, and
1
Z
5
x2 dx =
4
(4x2 − 9x) dx
(−4x2 ) dx
1
4
61
, calculate the following
3
8. Find the derivative of the following functions.
Z x
a) g(x) =
t3 dt
1
b) h(x) =
Z
x
Z
x2
2 −t
et
dt
3
c) k(x) =
√
1 + r 3 dr
0
9. Evaluate using u-substitution
Z
(15x − 27)(5x2 − 18x)10 dx
5
10. Evaluate
ln x
dx
x
Z
11. What is the average value of f (x) = 3e−x + x2 − 5 on the interval [3, 7]?
12. Find the area bounded by y = x2 − 5 and y = −x2 + 3 on [0, 3].
6
13. The daily marginal cost function for a local company is given by MC(x) = 2 + 0.02x where x
represents the number of ladders produced. If we know that it costs $750 to produce 50 ladders,
how much does it cost to produce 80 ladders?
14. Estimate
Z
1
(x2 + x + 1) dx by using the Riemann Sum with 5 subintervals and heights chosen
0
to be the left endpoint of each subinterval.
15. Evaluate
Z b
1
2
x
dx
4x − e +
x
1
7
16. Given the demand equation, D(x) = 70 − 0.2x, and the supply equation, S(x) = 13 + 0.0012x2 ,
what is the producers’ surplus at the equilibrium price level?
17. If f (x, y) = 2x2 y + y 3 x − 4xy + 8x − 4y, what is fxy ?
8