Question

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

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

Answer 1

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

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

Using LHR.

$\Rightarrow \underset{x\to 8}{lim}\frac{1}{2\sqrt{1+\sqrt{1+x}}}\times \frac{1}{2\sqrt{1+x}}\Rightarrow \frac{1}{2\sqrt{4}}\times \frac{1}{2\sqrt{9}}\Rightarrow \frac{1}{4\times 2\times 3}\Rightarrow \frac{1}{24}$