#### Answer

please see step-by-step

#### Work Step by Step

$\displaystyle \lim_{x\rightarrow a}f(x)=L$ if for every number $\epsilon > 0$ there is a number $\delta > 0$ such that the following is valid:
$($if $ 0 < |x-a| < \delta$ then $|f(x)-L| < \epsilon)$
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$f(x)=x.$
Given any $\epsilon > 0$, we want to find a $\delta > 0$ such that
$0 < |x-a| < \delta\ \ \Rightarrow\ \ |x-a| < \epsilon$.
So we take $\delta=\epsilon ,$
and, by the definition,
$\displaystyle \lim_{x\rightarrow a}x=a$