Answer
Yes, see the example below.
Work Step by Step
Yes, as an example
$$ f(x)=\frac{x^2-1}{x^2-x}$$
is not defined at $ x=1$; however, $$\lim\limits_{x \to 1}\frac{x^2-1}{x^2-x}=\lim\limits_{x \to 1}\frac{x+1}{x}=2.$$
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