MCQ
$\lim_{x \rightarrow 2} \frac{\sqrt{x-2}+\sqrt{x}-\sqrt{2}}{\sqrt{{{x}^{2}}-4}}=.......$
- ✓$\frac{1}{2}$
- B$1$
- C$2$
- Dએક પણ નહીં.
$\underset{x\to 2}{\mathop{\lim }}\,\frac{\sqrt{x-2}+\sqrt{x}-\sqrt{2}}{\sqrt{{{x}^{2}}-4}}\\=\lim_{x \rightarrow 2}\left\{\frac{1}{\sqrt{x+2}}+\frac{\sqrt{x}-\sqrt{2}}{\sqrt{x^2-4}}\right\}\\=\lim_{x \rightarrow 2}\frac{1}{\sqrt{x+2}}+\lim_{x \rightarrow 2}\frac{x-2}{(\sqrt{x}+\sqrt{2})\sqrt{(x+2)(x-2)}}\\=\frac{1}{2}+\lim_{x \rightarrow 2}\sqrt{\frac{(x-2)}{(x+2)}} \cdot \frac{1}{\sqrt{x}+\sqrt{2}}\\=\frac{1}{2}+0=\frac{1}{2}$
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