# Thread: Delta-Epsilon proof

1. ## Delta-Epsilon proof

I need help with this problem.

Show that $\lim_{x \to c} f(x)=L$ if and only if $\lim_{x \to 0} f(x+c)=L$

Thanks in advance

2. ## sufficient condition

Suppose that $lim_{x\rightarrow c}f(x)=L$ then $|x-c|<\delta\rightarrow|f(x)-L|=|f((x-c)+c)<\epsilon$, let r=x-c then
$|r-0|<\delta\rightarrow|f(r+c)-L|<\epsilon$, ie, $lim_{r\rightarrow 0}f(r+c)=L$
I hope you can solve the necessary part now.