## Calculus 8th Edition

See sec.1-8, Th.8: If f is continuous at b, and $\displaystyle \lim_{x\rightarrow a}g(x)=b,$ Then $\displaystyle \lim_{x\rightarrow a}f(\mathrm{g}(x))=f(\lim_{x\rightarrow a}\mathrm{g}(x))=f(b)$ ------------ Let $g(x)=4x^{2}-11$. Then, $\displaystyle \lim_{x\rightarrow 2}g(x)=16-11=5$, $\displaystyle \lim_{x\rightarrow 2}f(\mathrm{g}(x))=f(\lim_{x\rightarrow 2}\mathrm{g}(x))=f(5)=2$ The statement is true.