Chapter 2: Limits and Continuity - Section 2.4 - One-Sided Limits - Exercises 2.4 - Page 75: 16

$$-\frac{11}{2 \sqrt{6}} $$

\begin{aligned} \lim _{h \rightarrow 0^{-}} \frac{\sqrt{6}-\sqrt{5 h^{2}+11 h+6}}{h} &=\lim _{h \rightarrow 0^{-}}\left(\frac{\sqrt{6}-\sqrt{5 h^{2}+11 h+6}}{h}\right)\left(\frac{\sqrt{6}+\sqrt{5 h^{2}+11 h+6}}{\sqrt{6}+\sqrt{5 h^{2}+11 h+6}}\right) \\ &=\lim _{h \rightarrow 0^{-}} \frac{6-\left(5 h^{2}+11 h+6\right)}{h(\sqrt{6}+\sqrt{5 h^{2}+11 h+6})}\\ &=\lim _{h \rightarrow 0^{-}} \frac{-h(5 h+1)}{h(\sqrt{6}+\sqrt{5 h^{2}+11 h+6})}\\ &=\frac{-(0+11)}{\sqrt{6}+\sqrt{6}}\\ &=-\frac{11}{2 \sqrt{6}} \end{aligned}