ESE 318-01 Exam 3, Apr. 12, 2018
NAME:
___59 papers received from 60 enrolled__
Problem 1. (20 points)
Consider the scalar function
z
z
e
y
xy
e
x
z
y
x
F
2
2
2
2
,
,
and
the point
P
= (1, 1, 0).
(a)
Find the direction in which
F
is increasing fastest from
P
.
(b)
Find the rate of that maximum increase.
(c)
Find the rate of increase of
F
from
P
toward the point (-1,4,6).
(d)
Find
F
of
Laplacian
gradF
div
F
at
P
.
34
16
9
9
0
,
1
,
1
4
,
3
,
3
2
2
,
2
1
,
1
2
0
,
1
,
1
2
2
,
2
,
2
2
2
2
2
2
2
F
b
F
a
e
y
e
x
ye
x
y
xe
F
z
z
z
z
7
27
7
24
9
6
36
9
4
6
,
3
,
2
4
,
3
,
3
6
,
3
,
2
0
,
1
,
1
6
,
4
,
1
F
Dir
b
c
b
12
3
4
1
4
4
4
2
2
2
2
2
2
2
2
2
2
2
y
x
e
e
y
e
x
e
e
F
d
z
z
z
z
z
Grading: 21 papers earned all 20 points and another 18 earned 19 points with the only
error being to fail to evaluate the Laplacian at the point
P
. 5 points per part, in general.
Only 7 papers earned fewer than 16 points, and only 1 below 12.
Gradient or Laplacian not evaluated at
P
: -1 point.
“Sloppy” error:
-1 to -2 pts.
Sign error on (c) due to backward direction: -2 pts.
Method/approach seriously bad or botched: -3 to -5 pts per part.

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