X→ 8Lt√(1+√(1+x)) 2/x 8=x→ 8Lt√(1+x) x/ ( x 8 ) (√(1+√(1+x)) nbsp; +2 ) =x→ 8Lt1/ ( √(1+x)+3 ) ( √(1+√(1+x))+2 )=1/24 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Rationalization Method to Remove Indeterminate Form

limx→ 8√1+√1+...

Question

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

$\frac{3}{2}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\frac{1}{4}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\frac{1}{24}$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$\infty$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

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

$L t x \to 8 \frac{\sqrt{1 + \sqrt{1 + x}} - 2}{x - 8} = L t x \to 8 \frac{\sqrt{1 + x} - x}{(x - 8) (\sqrt{1 + \sqrt{1 + x}} + 2)} = L t x \to 8 \frac{1}{(\sqrt{1 + x} + 3) (\sqrt{1 + \sqrt{1 + x}} + 2)} = \frac{1}{24}$

Suggest Corrections

Similar questions

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

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

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

Evaluate: $lim x \to 0 ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \frac{{(1 + x)}^{\frac{1}{8}} - {(1 - x)}^{\frac{1}{8}}}{x} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦$

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

Join BYJU'S Learning Program