# Chapter 2 - Section 2.3 - Calculating Limits Using the Limit Laws - 2.3 Exercises: 38

$\lim\limits_{x\to1}g(x)=2$

#### 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 $\lim\limits_{x\to1}g(x)=2$

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