MCQ
$\lim_{x \rightarrow \infty} \left( \sqrt{x+\sqrt{x+\sqrt{x}}}-\sqrt{x} \right)=........$
- A${{e}^{4}}$
- B$\log 2$
- C$0$
- ✓$\frac{1}{2}$
$\lim_{x \rightarrow \infty}\left(\sqrt{x+\sqrt{x+\sqrt{x}}}-\sqrt x\right)$
$=\lim_{x \rightarrow \infty}\frac{\sqrt {x+\sqrt x}}{\sqrt{x+\sqrt{x+\sqrt{x}}}-\sqrt x}$
અંશ અને છેદને $\sqrt x$ થી ભાગતાં
$=\lim_{x \rightarrow \infty}\frac{\sqrt {1+ x^{\frac{-1}{2}}}}{\sqrt{1+\sqrt{{x^{\frac{-1}{2}}+{x^{\frac{-3}{2}}}}}+ 1}}$
$=\frac{1}{2}$
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