##<b>Unscramble the following definitions.</b> Let $f$ be a function defined on some open interval that contains the number $a$, except possibly at $a$ itself. #$\lim_{x\to a}\ f(x)=L$ $\Leftrightarrow$ for all $\epsilon>0$ there exists a $\delta>0$ such that if $0<|x-a|<\delta$ then $|f(x)-L|<\epsilon$ #$\lim_{x\to a^-}\ f(x)=L$ $\Leftrightarrow$ for all $\epsilon>0$ there exists a $\delta>0$ such that if $0<a-x<\delta$ then $|f(x)-L|<\epsilon$ #$\lim_{x\to a^+}f(x)=L$ $\Leftrightarrow$ for all $\epsilon>0$ there exists a $\delta>0$ such that if $0<x-a<\delta$ then $|f(x)-L|<\epsilon$ #$\lim_{x\to a}\ f(x)=\infty$ $\Leftrightarrow$ for all $M>0$ there exists a $\delta>0$ such that if $0<|x-a|<\delta$ then $f(x)>M$ #$\lim_{x\to a}\ f(x)=-\infty$ $\Leftrightarrow$ for all $N>0$ there exists a $\delta>0$ such that if $0<|x-a|<\delta$ then $f(x)<N$