# logarithmic function

• Apr 16th 2010, 08:59 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.
• Apr 17th 2010, 01:19 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?