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Question Number 214645 by efronzo1 last updated on 14/Dec/24

Answered by golsendro last updated on 15/Dec/24

$$=\underset{x\to 1}{\lim }\frac{\sqrt{4-3\mathrm{x}}-1}{\sqrt{\frac{1}{3-2\mathrm{x}}}-1}$$$$=\underset{x\to 1}{\lim }\frac{\sqrt{4-3\mathrm{x}}-1}{1-\sqrt{3-2\mathrm{x}}}.\sqrt{3-2\mathrm{x}}$$$$=1.\underset{x\to 1}{\lim }\frac{3-3\mathrm{x}}{2\mathrm{x}-2}.\frac{1+\sqrt{3-2\mathrm{x}}}{\sqrt{4-3\mathrm{x}}+1}$$$$=-\frac{3}{2}$$

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