Suppose the function $\displaystyle {g}$ statisfies

$\displaystyle {16}{x}-{2}{x}^{{2}}-{24}<{g{{\left({x}\right)}}}<{x}^{{2}}-{8}{x}+{24}$.

We want to use the Squeeze Theorem to evaluate $\displaystyle \lim_{{{x}\rightarrow{4}}}{g{{\left({x}\right)}}}$.

First evaluate: $\displaystyle \lim_{{{x}\rightarrow{4}}}{16}{x}-{2}{x}^{{2}}-{24}$
Preview Question 6 Part 1 of 3  

Next evaluate: $\displaystyle \lim_{{{x}\rightarrow{4}}}{x}^{{2}}-{8}{x}+{24}$
Preview Question 6 Part 2 of 3  

Therefore, by the Squeeze Theorem, $\displaystyle \lim_{{{x}\rightarrow{4}}}{g{{\left({x}\right)}}}$ = Preview Question 6 Part 3 of 3