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Question Number 192549 by cortano12 last updated on 20/May/23

$$\underset{x\to 0}{\lim }{\mathrm{x}}^2\tan \left(\frac{\sin \pi \mathrm{x}}{2\mathrm{x}}\right)=?$$

Answered by horsebrand11 last updated on 20/May/23

$$\underset{x\to 0}{\lim }{x}^2\tan \left(\frac{\sin \pi x}{2x}\right)$$$$=\underset{x\to 0}{\lim }{x}^2\tan \left(\frac{\pi x-\frac{{\pi }^3{x}^3}{6}}{2x}\right)$$$$=\underset{x\to 0}{\lim }{x}^2\tan (\frac{\pi }{2}-\frac{{\pi }^3{x}^2}{12})$$$$=\underset{x\to 0}{\lim }\frac{x^2}{\tan \left(\frac{{\pi }^3{x}^2}{12}\right)}=\frac{12}{{\pi }^3}$$

Answered by Gamil last updated on 20/May/23

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