Question

Solve the equation : ${lim}_{x\to 8}\frac{\sqrt{1+\sqrt{1+x}}-2}{x-8}=?$

• A. $\frac{3}{2}$
• B. $\frac{1}{4}$
• C. $\frac{1}{24}$
• D. $\frac{1}{5}$

Answer 1

The correct option is C $\frac{1}{24}$

$\underset{x\to 8}{lt}\frac{\sqrt{1+\sqrt{1+x}}-2}{x-8}$

$\underset{x\to 8}{lt}\frac{1}{2\sqrt{1+\sqrt{1+x}}}.\frac{1}{2\sqrt{1+x}}$

$=\frac{1}{2\sqrt{1+3}}.\frac{1}{2.3}=\frac{1}{4}.\frac{1}{6}=\frac{1}{24}$ [C]