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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$f(x)=c$.
Given any $\epsilon > 0$, we want to find a $\delta > 0$ such that
$ 0 < |x-a| < \delta\ \ \Rightarrow\ \ |c-c| < \epsilon$.
Since $|c-c|=0$, we can take $\delta$ to be any positive number,
because the conclusion is always true, regardless of the premise.
By the definition,
$\displaystyle \lim_{x\rightarrow a}c=c$
