Delta-Epsilon proof

**akolman** · August 22nd 2010, 05:53 PM

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

**facenian** · August 25th 2010, 02:31 AM

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.

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