Combinations of Functions In Exercises 35-38, find (a) f ( x ) + g ( x ) , (b) f ( x ) − g ( x ) , (c) f ( x ) ⋅ g ( x ) , (d) f ( x ) / g ( x ) , (e) f ( g ( x ) ) , and (f) g ( f ( x ) ) , if defined. See Example 5. f ( x ) = 2 x − 5 g ( x ) = 4 − 3 x
Combinations of Functions In Exercises 35-38, find (a) f ( x ) + g ( x ) , (b) f ( x ) − g ( x ) , (c) f ( x ) ⋅ g ( x ) , (d) f ( x ) / g ( x ) , (e) f ( g ( x ) ) , and (f) g ( f ( x ) ) , if defined. See Example 5. f ( x ) = 2 x − 5 g ( x ) = 4 − 3 x
Combinations of Functions In Exercises 35-38, find (a)
f
(
x
)
+
g
(
x
)
, (b)
f
(
x
)
−
g
(
x
)
, (c)
f
(
x
)
⋅
g
(
x
)
, (d)
f
(
x
)
/
g
(
x
)
, (e)
f
(
g
(
x
)
)
, and (f)
g
(
f
(
x
)
)
, if defined. See Example 5.
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 1 Solutions
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