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Question Number 145835 by mathdanisur last updated on 08/Jul/21

$$\underset{x\to \frac{\pi }{2}}{lim}(sin2x\cdot tgx)=?$$

Answered by bramlexs22 last updated on 09/Jul/21

$$\underset{x\to \frac{\pi }{2}}{\lim }\frac{2\sin \mathrm{x}\cos \mathrm{x}.\sin \mathrm{x}}{\cos \mathrm{x}}=\underset{x\to \frac{\pi }{2}}{\lim 2sin}{}^2\mathrm{x}$$$$=2\times 1=2$$

Answered by puissant last updated on 08/Jul/21

$${\lim }_{\mathrm{x}\to \frac{\pi }{2}}\frac{2\sin \left(\mathrm{x}\right)\cos \left(\mathrm{x}\right)\sin \left(\mathrm{x}\right)}{\cos \left(\mathrm{x}\right)}$$$$={\lim }_{\mathrm{x}\to \frac{\pi }{2}}{2\sin }^2\left(\mathrm{x}\right)={\lim }_{\mathrm{x}\to \frac{\pi }{2}}1-\cos \left(2\mathrm{x}\right)$$$$=1-(-1)=2...$$

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