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:
- A1
- B-1
- C0
- Dnone of these
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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If equation of a line is y = 3x - 4 then find the slope of line:
If x < 5, then.
$-\text{x} < – 5 $
$-\text{x}\leq-5$
$-\text{x} > – 5 $
$-\text{x}\leq-5$