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**ruprotein** (2) Show that $\displaystyle \lim_{x \to x_0} f(x) = L $ if and only if $\displaystyle \lim_{x \to 0} f(x+x_0) = L$. Assume $\displaystyle x_0$ and $\displaystyle L$ are finite.

(3) Show that if $\displaystyle \lim_{x \to x_0} f(x) = L$ and $\displaystyle E$ is a set which has $\displaystyle x_0$ as an accumulation point, then $\displaystyle \lim_{x \to x_0} f(x) = L$, $\displaystyle x \in E$. Give an example to show that the converse may fail. Assume $\displaystyle x_0$ and $\displaystyle L$ are finite.

can anyone solve any of these?