Definitions of Limits
Unscramble the following definitions of various types of limits.
Let $f$ be a function
defined on some open interval that contains the number $a,ドル 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ドル< |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ドル< 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ドル< 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ドル< |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ドル< |x-a|< \delta$ then $f(x)< N$