logarithmic function

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April 16th 2010, 07:59 PM
Kat-M

logarithmic function

how do i show that $\frac{d^2}{dx^2}\int_{-1} ^1 {log|x-t|}dt$ = $\int_{-1}^1 \frac{-1}{(x-t)^2}dt$ is INCORRECT?

i know that to interchange limit and integral, a function must be uniformly convergent to its limit. but i dont know exactly how to show it.
April 17th 2010, 12:19 AM
Prove It

Quote:

Originally Posted by Kat-M

how do i show that $\frac{d^2}{dx^2}\int_{-1} ^1 {log|x-t|}dt$ = $\int_{-1}^1 \frac{-1}{(x-t)^2}dt$ is INCORRECT?

i know that to interchange limit and integral, a function must be uniformly convergent to its limit. but i dont know exactly how to show it.

Can you differentiate an absolute value function at every point?

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