Ejercicios de repaso sección 5.3

Desarrolle cada función dada en una serie adecuada de cosenos o de senos.

  1. f(x)={0,π<x<0 1,0x<π\hspace{0.5cm} f(x)=\left\{\begin{matrix}0,&-{\pi}< x<0\\\ 1,&0\le x <{\pi}\\\end{matrix}\right.
  2. f(x)={1,π<x<0 2,0x<π\hspace{0.5cm} f(x)=\left\{\begin{matrix}-1,&-{\pi}< x<0\\\ 2,&0\le x <{\pi}\\\end{matrix}\right.
  3. f(x)={1,1<x<0 x,0x<1\hspace{0.5cm} f(x)=\left\{\begin{matrix}1,&-{1}< x<0\\\ x,&0\le x <{1}\\\end{matrix}\right.
  4. f(x)={0,1<x<0 x,0x<1\hspace{0.5cm} f(x)=\left\{\begin{matrix}0,&-{1}< x<0\\\ x,&0\le x <{1}\\\end{matrix}\right.
  5. f(x)=x+π,                        π<x<π\hspace{0.5cm} f(x)=x+\pi,\;\;\;\;\;\;\;\;\;\;\;\; -\pi < x < \pi