Ejercicios de repaso Capítulo 5

Encuentre la serie de Fourier de ff o la serie de senos y de cosenos en el intervalo dado

  1. f(x)={1,−5<x<0 1+x,0≤x<5\hspace{0.5cm} f(x)=\left\{\begin{matrix}1,&-{5}< x<0\\\ 1+x,&0\le x <{5}\\\end{matrix}\right.

  2. f(x)={2+x,−2<x<0 2,0≤x<2\hspace{0.5cm} f(x)=\left\{\begin{matrix}2+x,&-{2}< x<0\\\ 2,&0\le x <{2}\\\end{matrix}\right.

  3. f(x)={0,−π<x<0 ex−1,0≤x<π\hspace{0.5cm} f(x)=\left\{\begin{matrix}0,&-{\pi}< x<0\\\ e^x-1,&0\le x <{\pi}\\\end{matrix}\right.

  4. f(x)=3−2x,                        −π<x<π\hspace{0.5cm} f(x)=3-2x,\;\;\;\;\;\;\;\;\;\;\;\; -\pi < x < \pi

  5. f(x)=ex,                        −π<x<π\hspace{0.5cm} f(x)=e^x,\;\;\;\;\;\;\;\;\;\;\;\; -\pi < x < \pi

  6. f(x)={0,−2<x<0 x,0≤x<1 1,1≤x<2\hspace{0.5cm} f(x)=\left\{\begin{matrix}0,&-{2}< x<0\\\ x,&0\le x <{1}\\\ 1,&1\le x <{2}\\\end{matrix}\right.

  7. f(x)={0,−2<x<−1 −2,−1≤x<0 1,0≤x<1 0,1≤x<2\hspace{0.5cm} f(x)=\left\{\begin{matrix}0,&-{2}< x<-1\\\ -2,&-1\le x <{0}\\\ 1,&0\le x <{1}\\\ 0,&1\le x <{2}\\\end{matrix}\right.

  8. f(x)={x+1,−1<x<0 x−1,0≤x<1\hspace{0.5cm} f(x)=\left\{\begin{matrix}x+1,&-{1}< x<0\\\ x-1,&0\le x <{1}\\\end{matrix}\right.

  9. f(x)={x−1,−π<x<0 x+1,0≤x<π\hspace{0.5cm}f(x)=\left\{\begin{matrix}x-1,&-{\pi}< x<0\\\ x+1,&0\le x <{\pi}\\\end{matrix}\right.

  10. f(x)=π2−x2,                        −π<x<π\hspace{0.5cm}f(x)=\pi^2-x^2,\;\;\;\;\;\;\;\;\;\;\;\; -\pi < x < \pi

  11. f(x)=x3,                        −π<x<π\hspace{0.5cm}f(x)=x^3,\;\;\;\;\;\;\;\;\;\;\;\; -\pi < x < \pi

  12. f(x)=cosx,                        −π/2<x<π/2\hspace{0.5cm}f(x)=cos x,\;\;\;\;\;\;\;\;\;\;\;\; -\pi/2 < x < \pi/2

  13. f(x)={−π,−2π<x<−π x,−π≤x<π π,π≤x<2π\hspace{0.5cm} f(x)=\left\{\begin{matrix}-\pi,&-{2\pi}< x<-{\pi}\\\ x,&-{\pi}\le x <{\pi}\\\ \pi,&{\pi}\le x <{2\pi}\\\end{matrix}\right.

  14. f(x)={−1,−2<x<−1 −x,−1≤x<0 x,0≤x<1 1,1≤x<2\hspace{0.5cm} f(x)=\left\{\begin{matrix}-1,&-{2}< x<-1\\\ -x,&-1\le x <{0}\\\ x,&0\le x <{1}\\\ 1,&1\le x <{2}\\\end{matrix}\right.