Question

discuss whether the sequence {f_n(x)} where-\[f_n(x)=\int\limits\limits_{0}^{x}\frac{ e^{-t} }{ t^2+n }dt\\is~uniformly~convergent~Over,~~x \ge 0~\over\]

Answer 1

Sid is that you? =0P This is Will =0)

Answer 2

lol no :)

Answer 3

Ah ok

Answer 4

you need to show \[\rm \forall \epsilon \gt 0, \exists N ~s.t~ n\ge N \implies |f_n(x) - f(x)| \lt \epsilon \]

Answer 5

yes i know :) cauchy's criterion ,but i'm having difficulties there :(

Answer 6

I know nothing but could you show that \[\int_0^x\frac{e^{-t}}{t^2}\]
is uniformly convergent?

Answer 7

I have found this
http://prntscr.com/54k2fd

Answer 8

nice !

Answer 9

ohh it was easy!! thank you very much @ganeshie8