A) 1
B) 0
C) \[-1\]
D) None of these
Correct Answer: B
Solution :
\[\underset{x\to \infty }{\mathop{\lim }}\,\frac{\sqrt{{{x}^{2}}+1}-\sqrt[3]{{{x}^{3}}+1}}{\sqrt[4]{{{x}^{4}}+1}-\sqrt[5]{{{x}^{4}}+1}}\] \[=\underset{x\to \infty }{\mathop{\lim }}\,\frac{\sqrt{1+\frac{1}{{{x}^{2}}}}-\sqrt[3]{1+\frac{1}{{{x}^{3}}}}}{\sqrt[4]{1+\frac{1}{{{x}^{4}}}}-\sqrt[5]{\frac{1}{x}+\frac{1}{{{x}^{5}}}}}=\frac{1-1}{1-0}=0\]You need to login to perform this action.
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