# Delta-Epsilon proof

• Aug 22nd 2010, 06:53 PM
akolman
Delta-Epsilon proof
I need help with this problem.

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

• Aug 25th 2010, 03:31 AM
facenian
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.