Unscramble the following definitions of various types of limits. 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 $f(x)< N$