Answer
$1$
Work Step by Step
$\lim _{x\rightarrow 0}\dfrac {\arcsin x}{x}=\dfrac {\dfrac {d}{dx}\left( \arcsin x\right) }{\dfrac {d}{dx}\left( x\right) }=\dfrac {1}{\dfrac {\sqrt {1-x^{2}}}{1}}=\dfrac {1}{\sqrt {1-x^{2}}}=\dfrac {1}{\sqrt {1-0}}=1$
