In Exercises 59-70, the domain of each piecewise function is ( − ∞ , ∞ ) , a. Graph each function. b. Use your graph to determine the function's range. f ( x ) = { 2 x if x ≤ 0 2 if x > 0
In Exercises 59-70, the domain of each piecewise function is ( − ∞ , ∞ ) , a. Graph each function. b. Use your graph to determine the function's range. f ( x ) = { 2 x if x ≤ 0 2 if x > 0
Solution Summary: The author describes the function f(x) as a graph of 2 straight lines.
In Exercises 59-70, the domain of each piecewise function is
(
−
∞
,
∞
)
,
a.Graph each function.
b.Use your graph to determine the function's range.
f
(
x
)
=
{
2
x
if
x
≤
0
2
if
x
>
0
Definition Definition Group of one or more functions defined at different and non-overlapping domains. The rule of a piecewise function is different for different pieces or portions of the domain.
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
Precalculus, Books A La Carte Edition Plus MyLab Math with eText -- Access Card Package (6th Edition)
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