Answer
$4$
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:
$$ \lim\limits_{x \to 1} \dfrac{x^4-1}{x-1}=\lim\limits_{x \to 1} \dfrac{(x^2-1^2)(x^2+1^2)}{(x-1)} \\=\dfrac{\lim\limits_{x \to 1} (x-1)(x+1)(x^2+1)}{\lim\limits_{x \to 1} x-1} \\=\lim\limits_{x \to 1}(x+1) (x^2+1) \\=(1+1)(1+1)\\=(2)(2) \\=4$$
