## Calculus (3rd Edition)

The one-sided limits, $$\lim _{h \rightarrow 0^+}\frac{\sqrt{2+h}-2}{h}\frac{\sqrt{2+h}+2}{\sqrt{2+h}+2}=\lim _{h \rightarrow 0^+}\frac{h-2}{h\sqrt{2+h}+2}=\infty$$ $$\lim _{h \rightarrow 0^-}\frac{\sqrt{2+h}-2}{h}\frac{\sqrt{2+h}+2}{\sqrt{2+h}+2}=\lim _{h \rightarrow 0^-}\frac{h-2}{h\sqrt{2+h}+2}=-\infty$$ Hence the one-sided limits are not equal and infinite. The overall limit does not exist.