Ejercicios de repaso sección 5.3
Desarrolle cada función dada en una serie adecuada de cosenos o de senos.
f
(
x
)
=
{
0
,
−
π
<
x
<
0
1
,
0
≤
x
<
π
\hspace{0.5cm} f(x)=\left\{\begin{matrix}0,&-{\pi}< x<0\\\ 1,&0\le x <{\pi}\\\end{matrix}\right.
f
(
x
)
=
{
0
,
1
,
−
π
<
x
<
0
0
≤
x
<
π
f
(
x
)
=
{
−
1
,
−
π
<
x
<
0
2
,
0
≤
x
<
π
\hspace{0.5cm} f(x)=\left\{\begin{matrix}-1,&-{\pi}< x<0\\\ 2,&0\le x <{\pi}\\\end{matrix}\right.
f
(
x
)
=
{
−
1
,
2
,
−
π
<
x
<
0
0
≤
x
<
π
f
(
x
)
=
{
1
,
−
1
<
x
<
0
x
,
0
≤
x
<
1
\hspace{0.5cm} f(x)=\left\{\begin{matrix}1,&-{1}< x<0\\\ x,&0\le x <{1}\\\end{matrix}\right.
f
(
x
)
=
{
1
,
x
,
−
1
<
x
<
0
0
≤
x
<
1
f
(
x
)
=
{
0
,
−
1
<
x
<
0
x
,
0
≤
x
<
1
\hspace{0.5cm} f(x)=\left\{\begin{matrix}0,&-{1}< x<0\\\ x,&0\le x <{1}\\\end{matrix}\right.
f
(
x
)
=
{
0
,
x
,
−
1
<
x
<
0
0
≤
x
<
1
f
(
x
)
=
x
+
π
,
−
π
<
x
<
π
\hspace{0.5cm} f(x)=x+\pi,\;\;\;\;\;\;\;\;\;\;\;\; -\pi < x < \pi
f
(
x
)
=
x
+
π
,
−
π
<
x
<
π