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Question Number 140071 by EDWIN88 last updated on 04/May/21

$$\mathrm{For}\mathrm{what}\mathrm{value}\mathrm{of}\mathrm{k}\mathrm{is}\mathrm{the}\mathrm{following}$$ $$\mathrm{continous}\mathrm{function}?$$ $$\mathrm{f}\left(\mathrm{x}\right)=\{\begin{array}{l}\frac{\sqrt{7\mathrm{x}+2}-\sqrt{6\mathrm{x}+4}}{\mathrm{x}-2};\mathrm{if}\mathrm{x}⩾-\frac{2}{7}\mathrm{\&}\mathrm{x}\ne 2\\ \mathrm{k};\mathrm{if}\mathrm{x}=2\end{array}$$

Answered by bobhans last updated on 04/May/21

$$\underset{x\to 2}{\lim }\mathrm{f}\left(\mathrm{x}\right)=\underset{x\to 2}{\lim }\frac{\sqrt{7\mathrm{x}+2}-\sqrt{6\mathrm{x}+4}}{\mathrm{x}-2}$$ $$=\underset{x\to 2}{\lim }\frac{(\mathrm{x}-2)}{(\mathrm{x}-2)(\sqrt{7\mathrm{x}+2}+\sqrt{6\mathrm{x}+4})}$$ $$=\underset{x\to 2}{\lim }\frac{1}{\sqrt{7\mathrm{x}+2}+\sqrt{6\mathrm{x}+4}}=\frac{1}{8}=\mathrm{k}$$

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