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Question Number 194640 by cortano12 last updated on 12/Jul/23

$$\underbrace{}$$

Answered by horsebrand11 last updated on 12/Jul/23

$$\frac{1}{\sqrt{\mathrm{x}}}=\mathrm{y}$$$$\underset{\mathrm{y}\to 0}{\lim }\frac{1-\cos \frac{1}{2}\mathrm{y}}{\mathrm{y}\sin 3\mathrm{y}}=\underset{\mathrm{y}\to 0}{\lim }\frac{\sin {}^2\frac{1}{2}\mathrm{y}}{2\mathrm{y}\sin 3\mathrm{y}}$$$$=\frac{\left(\frac{1}{4}\right)}{6}=\frac{1}{24}$$

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