Calculating E infinity and P infinity - Stuart Pulliam (spulliam) - Rhea

$ x(t)=2t^2 $

$ E_{\infty} $

$ E_{\infty}=\int_{-\infty}^\infty |x(t)|^2\,dt $

$ E_{\infty}=\int_{-\infty}^\infty |2t^2|^2\,dt $

$ E_{\infty}=2\int_{-\infty}^\infty t^4\,dt $

$ E_{\infty}=\frac{2}{5}t^5|_{-\infty}^\infty $

$ E_{\infty}=\infty $

$ P_{\infty} $

$ P_{\infty}=\lim_{T \to \infty} \ \frac{1}{2T}\int_{-T}^{T}|x(t)|^2\,dt $

$ P_{\infty}=\lim_{T \to \infty} \ \frac{1}{2T}\int_{-T}^{T}|2t^2|^2\,dt $

$ P_{\infty}=\lim_{T \to \infty} \ \frac{1}{T}\int_{-T}^{T}t^4\,dt $

$ P_{\infty}=\lim_{T \to \infty} \ \frac{1}{5T}t^5|_{-T}^{T} $

$ P_{\infty}=\lim_{T \to \infty} \ \frac{1}{5T}[T^5 - (-T^5)] $

$ P_{\infty}=\lim_{T \to \infty} \ \frac{2T^5}{5T} $

$ P_{\infty}=\lim_{T \to \infty} \ \frac{2T^4}{5} $

$ P_{\infty}=\infty $