Exercises 55-58 refer to the following plot of some level curves of f ( x , y ) = c for c = − 2 , 0 , 2 , 4 , and 6. (Each grid square is 1 u n i t × 1 u n i t .) [ Hint: See Example 8.] At approximately which point or points does f appear to attain a maximum value?
Exercises 55-58 refer to the following plot of some level curves of f ( x , y ) = c for c = − 2 , 0 , 2 , 4 , and 6. (Each grid square is 1 u n i t × 1 u n i t .) [ Hint: See Example 8.] At approximately which point or points does f appear to attain a maximum value?
Exercises 55-58 refer to the following plot of some level curves of
f
(
x
,
y
)
=
c
for
c
=
−
2
,
0
,
2
,
4
, and 6. (Each grid square is
1
u
n
i
t
×
1
u
n
i
t
.) [Hint: See Example 8.]
At approximately which point or points does f appear to attain a maximum value?
4. Use method of separation of variable to solve the following wave equation
მłu
J²u
subject to
u(0,t) =0, for t> 0,
u(л,t) = 0, for t> 0,
=
t> 0,
at²
ax²'
u(x, 0) = 0,
0.01 x,
ut(x, 0) =
Π
0.01 (π-x),
0
Solve the following heat equation by method of separation variables:
ди
=
at
subject to
u(0,t) =0, for
-16024
ძx2 •
t>0, 0 0,
ux (4,t) = 0, for
t> 0,
u(x, 0) =
(x-3,
\-1,
0 < x ≤2
2≤ x ≤ 4.
ex
5.
important aspects.
Graph f(x)=lnx. Be sure to make your graph big enough to easily read (use the space given.) Label all
6
33
Chapter 8 Solutions
Student Solutions Manual for Waner/Costenoble's Applied Calculus, 7th
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