I need help with this problem.
Show that $\displaystyle \lim_{x \to c} f(x)=L$ if and only if $\displaystyle \lim_{x \to 0} f(x+c)=L$
Thanks in advance
Suppose that $\displaystyle lim_{x\rightarrow c}f(x)=L$ then $\displaystyle |x-c|<\delta\rightarrow|f(x)-L|=|f((x-c)+c)<\epsilon$, let r=x-c then
$\displaystyle |r-0|<\delta\rightarrow|f(r+c)-L|<\epsilon$, ie, $\displaystyle lim_{r\rightarrow 0}f(r+c)=L$
I hope you can solve the necessary part now.