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Question Number 142041 by nadovic last updated on 25/May/21

Answered by TheSupreme last updated on 25/May/21

$$\sqrt{-3a+b}-2=0$$$$b-3a=4$$$$\frac{-3a}{2\sqrt{-3a+b}}=-\frac{1}{4}$$$$6a=\sqrt{-3a+b}$$$$36a^2=-3a+b=4$$$$a^2=\frac{1}{9}$$$$a=\pm \frac{1}{3}$$$$b=4\pm 1$$$$\frac{\sqrt{\frac{x}{3}+5}-2}{x+3}$$$$\frac{\sqrt{-\frac{x}{3}+3}-2}{x+3}$$

Answered by iloveisrael last updated on 26/May/21

$$\left(1\right)form\frac{0}{0};\sqrt{b-3a}=2$$$$\Rightarrow b=4+3a$$$$\left(2\right)\underset{x\to -3}{\lim }\frac{\sqrt{ax+3a+4}-2}{x+3}=-\frac{1}{4}$$$$\Rightarrow \underset{x\to -3}{\lim }\frac{\frac{a}{2\sqrt{ax+3a+4}}}{1}=-\frac{1}{4}$$$$\Rightarrow \frac{a}{2\sqrt{4}}=-\frac{1}{4}\Rightarrow a=-1thenb=1$$$$$$

Answered by Willson last updated on 26/May/21

$$\underset{\mathrm{x}\to -3}{\lim }\frac{\frac{\mathrm{a}}{2\sqrt{\mathrm{ax}+\mathrm{b}}}}{1}=-\frac{1}{4}\Rightarrow \frac{\mathrm{a}}{\sqrt{\mathrm{b}-3\mathrm{a}}}=-\frac{1}{2}$$$$\mathrm{avec}\sqrt{\mathrm{b}-3\mathrm{a}}=2\mathrm{donc}\mathrm{a}=-1\mathrm{et}\mathrm{b}=1$$$$\underset{x\to -3}{\lim }\frac{\sqrt{1-\mathrm{x}}-2}{\mathrm{x}+3}=-\frac{1}{4}$$

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