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Question Number 34007 by rahul 19 last updated on 29/Apr/18

$$\underset{x\to 2}{\lim }\frac{\sqrt{x-2}+\sqrt{x}-\sqrt{2}}{\sqrt{x^2-4}}is?$$

Answered by tanmay.chaudhury50@gmail.com last updated on 29/Apr/18

$$=li\underset{x\to 2}{m}\frac{\sqrt{x-2}+(x-2)/(\sqrt{x}+\sqrt{2})}{\sqrt{(x+2)(x-2)}}$$$$takecommonfactor\sqrt{x-2}from{N}_{r}andDr$$$$=li\underset{x\to 2}{m}\frac{1+(\sqrt{x-2)}/(\sqrt{x}+\sqrt{2)}}{\sqrt{(x+2)}}$$$$=ansis1/2$$

Commented by rahul 19 last updated on 29/Apr/18

$$\mathcal{T}hankyousir.$$

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