Answer
$\lim\limits_{x\to 8}(1+\sqrt[3] x)(2-6x^2+x^3)=390$
Work Step by Step
$\lim\limits_{x\to 8}(1+\sqrt[3] x)(2-6x^2+x^3)$
$=\lim\limits_{x\to 8}(1+\sqrt[3]x)\times\lim\limits_{x\to 8}(2-6x^2+x^3)$ (product law)
$=[\lim\limits_{x\to 8}1+\lim\limits_{x\to 8}(\sqrt[3]x)]\times(\lim\limits_{x\to 8}2-\lim\limits_{x\to 8}6x^2+\lim\limits_{x\to 8}x^3)$ (sum and difference law)
$=[\lim\limits_{x\to 8}1+\sqrt[3]{(\lim\limits_{x\to 8}x)}]\times(\lim\limits_{x\to 8}2-6\lim\limits_{x\to 8}x^2+\lim\limits_{x\to 8}x^3)$ (root law and constant multiple law)
$=[1+\sqrt[3]8]\times(2-6\times8^2+8^3)$
$=390$
