(fixing mistake) |
(making pretty) |
||
| Line 1: | Line 1: | ||
<math>x(t)=\sqrt(2t)</math> | <math>x(t)=\sqrt(2t)</math> | ||
| + | ---- | ||
Compute <math>E\infty</math> | Compute <math>E\infty</math> | ||
| Line 18: | Line 19: | ||
<math>E\infty=\infty</math> | <math>E\infty=\infty</math> | ||
| + | ---- | ||
Compute <math>P\infty</math> | Compute <math>P\infty</math> | ||
Revision as of 18:37, 21 June 2009
$ x(t)=\sqrt(2t) $
Compute $ E\infty $
$ E\infty=\int_{-\infty}^\infty |x(t)|^2dt $
$ E\infty=\int_{-\infty}^\infty |\sqrt(2t)|^2dt $
$ E\infty=\int_{-\infty}^\infty |2t|dt $
$ E\infty=\int_{0}^\infty 2tdt $
$ E\infty=t^2|_{0}^{\infty} $
$ E\infty= \infty-0 $
$ E\infty=\infty $
Compute $ P\infty $
$ P\infty=\lim_{T \to \infty}\frac{1}{2*T}\int_{-T}^T |x(t)|^2dt $
$ P\infty=\lim_{T \to \infty}\frac{1}{2*T}\int_{-T}^T |\sqrt(2t)|^2dt $
$ P\infty=\lim_{T \to \infty}\frac{1}{2*T}\int_{-T}^T|2t|dt $
$ P\infty=\lim_{T \to \infty}\frac{1}{2*T}\int_{0}^T2tdt $
$ P\infty=\lim_{T \to \infty}\frac{|t^2|_{0}^{T}}{2*T} $
$ P\infty=\lim_{T \to \infty}\frac{T^2-0}{2*T} $
$ P\infty=\lim_{T \to \infty}\frac{T}{2} $
$ P\infty=\infty $
-Tylor Thompson
