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Question Number 200298 by Calculusboy last updated on 16/Nov/23

Commented by Frix last updated on 17/Nov/23

$$-\frac{1}{16}$$

Answered by Rasheed.Sindhi last updated on 17/Nov/23

$$\underset{x\to 4}{\lim }\frac{\frac{1}{\sqrt{x}}-\frac{1}{2}}{x-4}$$$$\underset{x\to 4}{\lim }\frac{\frac{2-\sqrt{x}}{2\sqrt{x}}}{(\sqrt{x}-2)(\sqrt{x}+2)}$$$$\underset{x\to 4}{\lim }\frac{-\cancel{(\sqrt{x}-2)}}{2\sqrt{x}\cancel{(\sqrt{x}-2)}(\sqrt{x}+2)}$$$$=\frac{-1}{2\sqrt{4}(\sqrt{4}+2)}=-\frac{1}{16}$$

Commented by Calculusboy last updated on 18/Nov/23

$$\mathit{t}\mathit{h}\mathit{a}\mathit{n}\mathit{k}\mathit{s}\mathit{s}\mathit{i}\mathit{r}$$

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