Answer
$\lim\limits_{x \to -2}(x^{3} -2x^{2} +4x +8) = - 16$
Work Step by Step
$\lim\limits_{x \to -2}(x^{3} -2x^{2} +4x +8) = \lim\limits_{x \to -2}x^{3} - 2 \lim\limits_{x \to -2}x^{2} + 4\lim\limits_{x \to -2}x + \lim\limits_{x \to -2}8$
= $-2^{3} - 2(-2)^{2} + 4*(-2) + 8$
$= -8 - 8 -8 + 8 $
$ = -16$
