MCQ
$\lim_{x \rightarrow 2}\frac{\sqrt{1+\sqrt{2+x}}-\sqrt{3}}{x-2}=.................$
- ✓$\frac{1}{8\sqrt{3}}$
- B$\frac{1}{4\sqrt{3}}$
- C$0$
- Dએક પણ નહીં.
$\lim_{x \rightarrow 2}\frac{\sqrt{1+\sqrt{2+x}}-\sqrt{3}}{x-2}$
$=\lim_{x \rightarrow 2}\frac{1+\sqrt{2+x}-3}{(\sqrt{1+\sqrt{2+x}}+\sqrt{3})(x-2)}$
$=\lim_{x \rightarrow 2}\frac{\sqrt{2+x}-2}{(\sqrt{1+\sqrt{2+x}}+\sqrt{3})(x-2)}$
$=\lim_{x \rightarrow 2}\frac{2+x--4}{(\sqrt{1+\sqrt{2+x}}+\sqrt{3})(\sqrt{2+x}+2)(x-2)}$
$=\lim_{x \rightarrow 2}\frac{1}{(\sqrt{1+\sqrt{2+x}}+\sqrt{3})(\sqrt{2+x}+2)}$
$=\frac{1}{(\sqrt{1+\sqrt{2+2}}+\sqrt{3})}\cdot \frac{1}{\sqrt{2+2}+2}$
$=\frac{1}{\sqrt{1+2}+\sqrt{3}}\cdot \frac{1}{2+2}$
$=\frac{1}{2\sqrt{3}}\cdot \frac{1}{4}$
$=\frac{1}{8\sqrt{3}}$
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