MCQ
$ \lim_\limits{\text{x} \rightarrow\infty}\frac{\sqrt{\text{x}^2+1}-^3\sqrt{\text{x}^2+1}}{^4\sqrt{\text{x}^4+1}-^5\sqrt{\text{x}^4+1}}$ is equal to:
  • A
    1
  • B
    -1
  • C
    0
  • D
    none of these

Answer

  1. 1

Solution:

$ \lim_\limits{\text{x} \rightarrow\infty}\frac{\sqrt{\text{x}^2+1}-^3\sqrt{\text{x}^2+1}}{^4\sqrt{\text{x}^4+1}-^5\sqrt{\text{x}^4+1}}$

$ =\displaystyle \lim_{\text{x}\rightarrow \infty}\frac {\sqrt {1+1/\text{x}^2}-\sqrt [3]{1/\text{x}+1/\text{x}^3}}{\sqrt [4]{1+1/\text{x}^4}-\sqrt [5]{1/\text{x}-1/\text{x}^5}}$

$ =\frac{1-0}{1-0}=1$

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