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Question Number 106983 by Khalmohmmad last updated on 08/Aug/20

Answered by bemath last updated on 08/Aug/20

Answered by Dwaipayan Shikari last updated on 08/Aug/20

$$\underset{x\to 0}{\lim }(\frac{3^{\pi x}cosx}{sinx}-\frac{{cos}^{2}x}{sinx})$$$$\underset{x\to 0}{\lim }\frac{cosx}{sinx}(3^{\pi x}-cosx)=\underset{x\to 0}{\lim }\frac{\pi x}{tanx}\left(\frac{3^{\pi x}-cosx}{\pi x}\right)$$$$\underset{x\to 0}{\lim }\frac{\pi xcosx}{x}\left(\frac{3^{\pi x}-1}{\pi x}\right)cosx\to 1$$$$\underset{x\to 0}{\lim }\pi cosxlog\left(3\right)=\pi log\left(3\right)$$$$$$

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