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Question Number 23688 by A1B1C1D1 last updated on 04/Nov/17

Answered by $@ty@m last updated on 04/Nov/17

$$Usemethodofrationalization$$$$=\underset{x\to 0}{\lim }\frac{x^2(\sqrt{x^2+12}+\sqrt{12})}{x^2+12-12}$$$$=\underset{x\to 0}{\lim }\frac{x^2(\sqrt{x^2+12}+\sqrt{12})}{x^2}$$$$=\underset{x\to 0}{\lim }(\sqrt{x^2+12}+\sqrt{12})$$$$=\sqrt{12}+\sqrt{12}$$$$=2\sqrt{12}$$$$=4\sqrt{3}$$

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