There are two useful inverse trigonometric limit rules in calculus. Firstly, learn the limit properties and you will know how limits of inverse trigonometric functions are used for dealing inverse trigonometric functions in calculus.

$(1) \,\,\,\,\,\,$ $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{\sin^{-1}{x}}{x}} \,=\, 1$

$(2) \,\,\,\,\,\,$ $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{\tan^{-1}{x}}{x}} \,=\, 1$

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