Answer
390
Work Step by Step
$\displaystyle \lim_{x\rightarrow 8}(1+\sqrt[3]{x})(2-6x^{2}+x^{3})$=
...Law 4 (product ),
$=\displaystyle \lim_{x\rightarrow 8}(1+\sqrt[3]{x})\cdot\lim_{x\rightarrow 8}(2-6x^{2}+x^{3})$ =
...Laws 1 (sum), 2 (difference), and 3 (constant multiple)
$=(\displaystyle \lim_{x\rightarrow 8}1+\lim_{x\rightarrow 8}\sqrt[3]{x})\cdot(\lim_{x\rightarrow 8}2-6\lim_{x\rightarrow 8}x^{2}+\lim_{x\rightarrow 8}x^{3})$ =
...Laws
7:($\displaystyle \lim_{x\rightarrow a}c=c$), 10: ( $\displaystyle \lim_{x\rightarrow \mathit{0}}\sqrt[n]{x}=\sqrt[n]{a}$), and 9: $( \displaystyle \lim_{x\rightarrow a}x^{n}=a^{n})$,
$=(1+\sqrt[3]{8})\cdot(2-6\cdot 8^{2}+8^{3})$
$=(3)(130)$
$=390$
