Name:
Section:
MATH 25
Unit 4 Problem Set
Directions: Answer the following COMPLETELY, NEATLY, and ORDERLY. Submit
your answers (in pdf format) through our google classroom.
1. The volume V of a right circular cone of radius r and height h is given by V = 31 πr2 h.
(2 points each)
(a) Find a formula for the instantaneous rate of change of V with respect to r if
r changes and h remains constant.
(b) Find a formula for the instantaneous rate of change of V with respect to h if
h changes and r remains constant.
2. Given f (x, y, z) = xexy + sin(xyz), find fyzz . (7 points)
3. A manufacturer supplies refrigerators to two stores, A and B. The manager estimates that if x refrigerators are delivered to store A and y units to store B each
month, the monthly profit will be P (x, y) pesos, where
P (x, y) = −2x2 − 3xy − 2y 2 + 20x + 40y − 300.
Each month, the company can produce exactly 700 refrigerators. How many refrigerators should be supplied to store A and how many to store B in order to maximize
monthly profit? (7 points)
4. LetR be the region shown in the accompanying figure. Fill in the missing limits of
integration. (8 points)
ZZ
Z 4Z Z 5Z (a)
f (x, y) dA =
f (x, y) dydx +
f (x, y) dydx
R
2
ZZ
Z
4
Z
f (x, y) dA =
(b)
R
f (x, y) dxdy
5. SET-UP the double integral that solves for the volume of the solid z = 9 − x2 − y 2
on the first octant using dydx. (4 points)
Total: 30 pts
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