JEE MainMathematicsEasyLimits

$\lim_{x \rightarrow \infty}\mspace{2mu}\frac{\sqrt{x^{2} + 1} - \sqrt[3]{x^{3} + 1}}{\sqrt[4]{x^{4} + 1} - \sqrt[5]{x^{4} + 1}}$
equals

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\lim_{x \rightarrow \infty}\mspace{2mu}\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

Source: Grass-G / M-19 Mathematics Paper 28 Nov Fourth.docx

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