Revision as of 06:51, 17 June 2009 by Rrayburn (Talk | contribs)

$ x(t)=\sqrt{t} $


$ E\infty=\int|x(t)|^2dt $ (from $ -\infty $ to $ \infty $)

   $ E\infty=\int|\sqrt{t}|^2dt=\int tdt $(from $ 0 $ to $ \infty $ due to sqrt limiting to positive Real numbers)
   $ E\infty=.5*t^2| $(from $ 0 $ to $ \infty $)
   $ E\infty=.5(\infty^2-0^2)=\infty $

$ P\infty=lim\bullet T\rightarrow\infty*1/(2T)\int|x(t)|^2dt $ (from $ -T $ to $ T $)

   $ P\infty=lim\bullet T\rightarrow\infty*1/(2T)\int|\sqrt{t}|^2dt=\int tdt $ (from $ 0 $ to $ T $)
   $ P\infty=lim\bullet T\rightarrow\infty*1/(2T)*.5t^2| $(from $ 0 $ to $ T $)
   $ P\infty=lim\bullet T\rightarrow\infty*1/(2T)*(.5T^2) $

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Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett