Question

Solve:
$\underset{x\to 8}{lim}\frac{\sqrt{1+\sqrt{1+x}}-2}{x-8}$

Answer 1

${lim}_{x\to 8}\frac{\sqrt{1+\sqrt{1+x}}-2}{x-8}$

$={lim}_{x\to 8}\frac{1}{(\sqrt{x+1}+3)(\sqrt{1\sqrt{1+x}}+2)}$

$=\frac{1}{(3+3)(2+2)}$

$=\frac{1}{24}$