Answer
$\lim\limits_{x\to1}g(x)=2$
Work Step by Step
Consider the following limits:
$\lim\limits_{x\to1}2x=2\times1=2$
$\lim\limits_{x\to1}(x^4-x^2+2)=1^4-1^2+2=2$
So, $\lim\limits_{x\to1}2x=\lim\limits_{x\to1}(x^4-x^2+2)=2$
We also know that $2x\leq g(x)\leq(x^4-x^2+2)$ for all $x$
Therefore, applying the squeeze theorem, we find
$\lim\limits_{x\to1}g(x)=2$
