Chapter 2: Limits and Continuity - Section 2.2 - Limit of a Function and Limit Laws - Exercises 2.2 - Page 57: 64

$2$

Here, we have $\lim\limits_{x\to0}(2-x^2)=2-0^2=2$ and $\lim\limits_{x\to0}(2\cos x)=2\times\cos0=2\times1=2$ So, the both side limits are same. As we can see that $2-x^2\le g(x)\le 2\cos x$ for all $x$ Thus, as per Sandwich Theorem, we have found that $\lim\limits_{x\to0}g(x)=2$