$5.00 solution
- This tutorial was purchased 1 time and rated A+ by students like you.
- Posted on Feb 05, 2009 at 03:56:19PM
A:
Preview: ... r changing the variables you get the integral<br><br>2/pi int from 0 to infinity of f(ut)/(1+t^2)dt<br><br>Now, f(ut)/(1+t^2) goes uniformly to f(0)/(1+t^2) since f is bounded, therefore<br>the integral goes to<br><br>2/pi int form 0 to infinity of f(0)/(1+t^2)=f(0)*2/pi*int from 0 to infinity of 1/(1+t^2)<br>=f(0)<br><br>since int from 0 to infinity of 1/(1+t^2) =pi/2<br><br>(here we use the fact that an antiderivative of 1/(1+t^2)<br>is arctan(t)<br><br>second circled problem:<br><br>Denote F(x)= int from 0 to inf of e^(-u^2)cos(xu)du ...
The full tutorial is about 274 words long plus attachments.
Attachments:
problems.pdf (32K) (Preview)