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

Question

anonymous · Answer

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

sidsiddhartha · Answer

lol no :)

anonymous · Answer

Ah ok

rsadhvika · Answer

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

sidsiddhartha · Answer

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

thomas5267 · Answer

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

ganeshie8 · Answer

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

ikram002p · Answer

nice !

sidsiddhartha · Answer

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