Goal:
$\displaystyle \forall M>0,\exists\delta>0$ such that
$\displaystyle 0<|x-0|<\delta\Rightarrow \frac1{x^2}>M$
Guess:
$\displaystyle |x|<\delta$
$\displaystyle |x|^2<\delta^2$
$\displaystyle \frac1{x^2}>\frac1{\delta^2}$
Sol: 주어진 M>0에 대하여
$\displaystyle \delta=\frac1{\sqrt{M}}$ 이라 하면,
$\displaystyle 0<|x|<\delta\Rightarrow |x|<\frac1{\sqrt{M}}$
$\displaystyle \Rightarrow x^2<\frac1{M}$
$\displaystyle \Rightarrow \frac1{x^2}>M$