Q. $\lim_{x \rightarrow \infty}\frac{\sqrt{x^{2} + 1} - \sqrt[3]{x^{3} + 1}}{\sqrt[4]{x^{4} + 1} - \sqrt[5]{x^{4} + 1}}$ equals
A) 1
B) 0
C) -1
D) None of these
Explanation
(b)
$\lim_{x \rightarrow \infty}\frac{\sqrt{x^{2} + 1} - \sqrt[3]{x^{3} + 1}}{\sqrt[4]{x^{4} + 1} - \sqrt[5]{x^{4} + 1}}$
$= \lim_{x \rightarrow \infty}\frac{\sqrt{1 + \frac{1}{x^{2}}} - \sqrt[3]{1 + \frac{1}{x^{3}}\ }}{\sqrt[4]{1 + \frac{1}{x^{4}}} - \sqrt[5]{\frac{1}{x} + \frac{1}{x^{5}}}} = \frac{1 - 1}{1 - 0} = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.