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Question Number 107710 by bemath last updated on 12/Aug/20

$$✓\frac{\mathcal{B}e\mathcal{M}ath✓}{cooll}$$$$\underset{x\to \mathrm{\infty }}{\lim }{\left(\frac{x+5}{x-3}\right)}^{\frac{3x+1}{\cos 2x}}?$$

Answered by Dwaipayan Shikari last updated on 12/Aug/20

$$\underset{x\to \mathrm{\infty }}{\lim }{(1+\frac{8}{x-3})}^{\frac{8}{x-3}.\frac{x-3}{8}.\frac{3x+1}{cos2x}}=y$$$$e^{\frac{8}{x-3}.\frac{3x+1}{cos2x}}=e^{\frac{8}{1-\frac{3}{x}}.\frac{3+\frac{1}{x}}{cos2x}}=e^{\frac{24}{cos2x}}$$$$As-1⩽cos2x⩽1$$

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