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Question Number 176808 by cortano1 last updated on 27/Sep/22

$$\underset{x\to \mathrm{\infty }}{\lim }\frac{\sin \mathrm{x}}{1+\cos {}^2\mathrm{x}}=?$$

Answered by TheHoneyCat last updated on 08/Oct/22

$$\mathrm{let}n\in \mathbb{Z}$$$$\frac{\sin \left(2\pi n\right)}{1+{\cos }^2\left(2\pi n\right)}=\frac{0}{1+1^2}=0$$$$\frac{\sin (\pi /2+2\pi n)}{1+{\cos }^2(\pi /2+2\pi n)}=\frac{1}{1+0}=1$$$$$$$$\mathrm{So}\mathrm{there}\mathrm{exists}\mathrm{no}\mathrm{such}\mathrm{limit}$$

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