Answer
$\lim\limits_{x \to 2}\dfrac{x^{3}-8}{x-2}=12$
Work Step by Step
$\lim\limits_{x \to 2}\dfrac{x^{3}-8}{x-2}$
Factor the numerator and simplify:
$\lim\limits_{x \to 2}\dfrac{x^{3}-8}{x-2}=\lim\limits_{x \to 2}\dfrac{(x-2)(x^{2}+2x+4)}{x-2}=\lim\limits_{x \to 2}x^{2}+2x+4=...$
Apply direct substitution to evaluate the limit:
$\lim\limits_{x \to 2}x^{2}+2x+4=(2)^{2}+2(2)+4=12$
