MCQ
$\lim_{x \rightarrow \infty} \frac{\sqrt{{{x}^{2}}+1}-\sqrt[3]{{{x}^{3}}+1}}{\sqrt[4]{{{x}^{4}}+1}-\sqrt[5]{{{x}^{5}}+1}}=.......$
- A$-1$
- ✓$0$
- C$1$
- Dએક પણ નહી.
$\underset{x\to \infty }{\mathop{\lim }}\,\frac{\sqrt{{{x}^{2}}+1}-\sqrt[3]{{{x}^{3}}+1}}{\sqrt[4]{{{x}^{4}}+1}-\sqrt[5]{{{x}^{5}}+1}}\\=\underset{x\to \infty }{\mathop{\lim }}\,\frac{\sqrt{1+\frac{1}{x^2}}-\sqrt[3]{1+\frac{1}{{x}^{3}}}}{\sqrt[4]{1+\frac{1}{{x}^{4}}}-\sqrt[5]{1+\frac{1}{{x}^{5}}}}\\=\frac{\sqrt{1+0}-\sqrt[3]{1+0}}{\sqrt[4]{1+0}-\sqrt[5]{1+0}}$
$=0$
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