The correct option is B 0 lim_x →∞{√(x^2+√(x^4+1)) √(2)x} lim_x →∞ #160;√(x^4+1) x^2/(√(x^2+√(x^4+1))+√(2x)) lim_x →∞1/(√(x^2+√(x^4+1))+√ ...

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

Rationalization Method to Remove Indeterminate Form

limx →∞√x2+√x...

Question

$lim x \to \infty {\sqrt{x^{2} + \sqrt{x^{4} + 1}} - \sqrt{2} x}$

\infty

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

0

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

2

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

1

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

Open in App

Solution

The correct option is B $0$
$lim x \to \infty {\sqrt{x^{2} + \sqrt{x^{4} + 1}} - \sqrt{2} x}$
$lim x \to \infty \frac{\sqrt{x^{4} + 1} - x^{2}}{(\sqrt{x^{2} + \sqrt{x^{4} + 1}} + \sqrt{2 x})}$
$lim x \to \infty \frac{1}{(\sqrt{x^{2} + \sqrt{x^{4} + 1}} + \sqrt{2 x}) (\sqrt{x^{4} + 1} + x^{2})}$
$lim x \to \infty \frac{1}{x^{3} (\sqrt{1 + \sqrt{1 + \frac{1}{x^{4}}}} + \sqrt{2}) (\sqrt{1 + \frac{1}{x^{4}}} + 1)}$
$= 0$

Suggest Corrections

Similar questions

Evaluate the following one sided limits:

$(i) {lim}_{x \to 2^{+}} \frac{x - 3}{x^{2} - 4}$

$(i i) {lim}_{x \to 2^{-}} \frac{x - 3}{x^{2} - 4}$

$(i i i) {lim}_{x \to 0^{+}} \frac{1}{3 x}$

$(i v) {lim}_{x \to 8^{+}} \frac{2 x}{x + 8}$

$(v) {lim}_{x \to 0^{+}} \frac{2}{x^{\frac{1}{5}}}$

$(v i) {lim}_{x \to \frac{π^{-}}{2}} t a n x$

$(v i i) {lim}_{x \to \frac{π}{2^{+}}} s e c x$

$(v i i i) {lim}_{x \to 0^{-}} \frac{x^{2} - 3 x + 2}{x^{3} - 2 x^{2}}$

$(i x) {lim}_{x \to - 2^{+}} \frac{x^{2} - 1}{2 x + 4}$

$(x) {lim}_{x \to 0^{+}} (2 - c o t x)$

$(x i) {lim}_{x \to 0^{-}} 1 + c o s e c x$

lim x \to 0 \frac{x (e^{(\sqrt{1 + x^{2} + x^{4}} - 1) / x} - 1)}{\sqrt{1 + x^{2} + x^{4}} - 1}

$l i m x \to \infty \frac{\sqrt{x^{2} + 1} - \sqrt[3]{x^{2} + 1}}{\sqrt[4]{x^{4} + 1} - \sqrt[5]{x^{4} - 1}} i s e q u a l t o$

lim x \to \infty \frac{\sqrt{x^{2} + 1} - \sqrt[3]{x^{2} + 1}}{\sqrt[4]{x^{4} + 1} - \sqrt[5]{x^{4} - 1}}

lim x \to 1 \frac{x^{8} - 2 x + 1}{x^{4} - 2 x + 1}

Join BYJU'S Learning Program