Answer
$$3$$
Work Step by Step
In order to simplify the given expression, we will use the following rules.
$(a) \lim\limits_{x \to a} \dfrac{p(x)}{q(x)}=\dfrac{\lim\limits_{x \to a} p(x)}{\lim\limits_{x \to a} q(x)} \\ (b) \lim\limits_{x \to a} k(x)=k(a)$ ;
where $a$ is a constant.
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Thus, we have:
$$ \lim\limits_{x \to 2} \dfrac{(x^3-8)}{x^2-4}=\lim\limits_{x \to 2} \dfrac{(x^3-2^3)}{(x^2-2^2)} \\=\dfrac{\lim\limits_{x \to 2} (x-2)(x^2+2x+4)}{\lim\limits_{x \to 2} (x-2)(x+2)}\\=\dfrac{\lim\limits_{x \to 2} (x^2+2x+4)}{\lim\limits_{x \to 2} (x+2)} \\=\dfrac{4+4+4}{2+2} \\=3$$
