Math 237
Assignment 5
Due: Friday, Oct 22nd
1.
Let
f
(
x, y
) = ln(
x
2
+
y
2
).
a) Find the directional derivative of
f
at (

1
,
2) in the direction of the vector
~v
= (3
,

4).
b) Find the direction in which
f
is increasing the fastest at (1
,
1). What is the magnitude
of this rate of change?
c) Find the equation of the tangent line at (1
,
1) to the level curve
f
(
x, y
) = ln 2.
2.
A spaceship cruising on the sunny side of the planet Venus starts to overheat. The
spaceship is located at (1
,

1
,
1) and the temperature of the ship’s hull when at location
(
x, y, z
) will be
T
= 200 +
e

x
2

2
y
2

3
z
2
, where
x
,
y
,
z
are in meters.
a) In what direction should the ship proceed in order to decrease the temperature the
quickest.
b) If the ship travels at
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This note was uploaded on 12/10/2010 for the course MATH 237 taught by Professor Wolczuk during the Spring '08 term at Waterloo.
 Spring '08
 WOLCZUK
 Derivative

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