http://i291.photobucket.com/albums/l...Capture123.jpg

is this true or false? Explain why. I think it is not true because the interval is unbounded. However, I cannot explain why.

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- Nov 4th 2009, 02:13 PMxyzuniform convergence
http://i291.photobucket.com/albums/l...Capture123.jpg

is this true or false? Explain why. I think it is not true because the interval is unbounded. However, I cannot explain why. - Nov 4th 2009, 05:32 PMTheEmptySet
- Nov 4th 2009, 06:05 PMxyzuniform convergence
If thats true, I am not quite sure how this problem is done. The complete problem is

http://i291.photobucket.com/albums/l.../Capture34.jpg

I appreciate your help a lot. The next thing, is to take limit of n on both sides. Does that mean right hand limit at 0 and left hand limit at 0? Please let me know how the problem ends up with 1 as value of integral when it should be 0? - Nov 4th 2009, 06:32 PMredsoxfan325
It's true that uniform convergence allows you to interchange the limit and the integral, but only on a bounded interval $\displaystyle [a,b]$. (The proof of the theorem uses the value $\displaystyle b-a$, which makes no sense if $\displaystyle b=\infty$.)