CALCULUS 2302 FALL 2012
PRACTICE QUESTIONS FOR THE FINAL
Note: problems are taken from the previous nals.
7.1. Consider the function f (x, y) = 4 + (x 1)2 + (y 1)2 on the triangular region where
x 0, y 0, and y 4 x. Find the absolute maximum and absolute
CALCULUS 2302 FALL 2012
HOMEWORK ASSIGNMENT 2.
Due October 3.
1.1. Find the acute angle between two lines in R2 given by
x + 2y = 7
1.2.
1.3.
1.4.
1.5.
1.6.
5x y = 2
(i) Given the vector u = 3i + 5j 3k, nd a scalar c such that the scalar projection of u
o
CALCULUS 2302 FALL 2012
HOMEWORK ASSIGNMENT 4.
Due November 5.
4.1. Find a vector function that represents the curve of intersection of the surfaces z = 4x2 + y 2
and z = xy.
4.2. Prove the Chain Rule for vector-valued functions:
d
[u(f (t)] = f (t) u (f
CALCULUS 2302 FALL 2012
HOMEWORK ASSIGNMENT 6.
Due December 3.
6.1. If u = f (x, y), where x = es cos t and y = es sin t, show that
2u 2u
+ 2 = e2s
x2
y
2u 2u
+ 2
s2
t
.
6.2. Find the directions in which the directional derivative of f (x, y) = yexy at th