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Limits and Derivatives — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsLimits and Derivatives1 Mark
MCQ
$\lim_\limits{\text{x} \rightarrow \infty}\frac{2\sqrt{\text{x}}+3\sqrt[3]{\text{x}}+4\sqrt[4]{\text{x}}+...+\text{n}\sqrt[\text{n}]{\text{x}}}{\sqrt{(2\text{x}-3}+{\sqrt[3]{(2\text{x}-3)}+{\sqrt[4]{(2\text{x}-3)}+...+}{\sqrt[\text{n}]{(2\text{x}-3)}}}}$ is equal to:
  • A
    $1$
  • B
    $2$
  • ✓
    $\sqrt{2}$
  • D
    None of these
✓

Answer

Correct option: C.
$\sqrt{2}$
$ \lim_\limits{\text{x} \rightarrow \infty}\frac{2\sqrt{\text{x}}+3\sqrt[3]{\text{x}}+4\sqrt[4]{\text{x}}+...+\text{n}\sqrt[\text{n}]{\text{x}}}{\sqrt{(2\text{x}-3}+{\sqrt[3]{(2\text{x}-3)}+{\sqrt[4]{(2\text{x}-3)}+...+}{\sqrt[\text{n}]{(2\text{x}-3)}}}}$
Dividing numerator and denominator by$ \sqrt{\text{x}}$
$=\frac{2}{\sqrt{2}}$
$=\sqrt{2}$

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