$\lim \frac{(5+\sqrt{x+1}-8)(\sqrt{2x}+4)}{({{(\sqrt[3]{5+\sqrt{x+1}})}^{2}}+2\left( \sqrt[3]{5+\sqrt{x+1})}+4 \right)(2x-16)}$ $\underset{x\to 8}{\mathop{\lim }}\,\frac{8(\sqrt{x+1}-3)}{24(x-8)}=\frac{1}{3}\underset{x\to 8}{\mathop{\lim }}\,\frac{x+1-9}{(x-8)(\sqrt{x+1}+3)}=\frac{1}{18}$