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Question Number 197514 by cortano12 last updated on 20/Sep/23

$$\underset{x\to \mathrm{\infty }}{\lim }\sin \mathrm{x}{\sin }^{-1}\left(\frac{1}{\mathrm{x}}\right)=?$$

Answered by MM42 last updated on 20/Sep/23

$$\frac{1}{x}=t\Rightarrow {lim}_{t\to 0}sin\frac{1}{t}\times {sin}^{-1}t=0$$$$tip‘‘ifx\to a;\mid f\mid <k\mathrm{\&}{lim}_{x\to a}g=0\Rightarrow {lim}_{x\to a}f\times g=0{}^{″}$$

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