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Question Number 162103 by HongKing last updated on 26/Dec/21

$$\mathrm{Find}:$$$$\underset{\mathbf{x}\to 0}{\lim }\frac{\mathrm{sinx}-{\sin }^{-1}\mathrm{x}}{\mathrm{sinhx}-{\sinh }^{-1}\mathrm{x}}=?$$

Answered by Ar Brandon last updated on 26/Dec/21

$$\underset{x\to 0}{\lim }\frac{x-(x-\frac{x^3}{6})}{x-(x+\frac{x^3}{6})}=\underset{x\to 0}{\lim }\frac{\frac{x^3}{6}}{-\frac{x^3}{6}}=-1$$

Commented by HongKing last updated on 28/Dec/21

$$\mathrm{thank}\mathrm{you}\mathrm{dear}\mathrm{Sir}$$

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