Using the defenition of a limit, show this: $\lim_{x\rightarrow a} f(x)= \lim_{h\rightarrow 0}f(a+h)$ when at least one of the two limits exist.
Given $f: \Bbb R\rightarrow\Bbb R$ and a point $a\in\Bbb R$. Prove $lim_{x\rightarrow a} f(x)=\lim_{h\rightarrow 0} f(a+h)$ if 1 of the limits exists.