Find the limit of function (xarcsinxsin1 / x) / SiNx when x tends to 0

(xarcsinxsin1/x)/sinx
=lim x/sinx *lim arcsinxsin1/x
=1*lim (arcsinx/x ) *xsin1/x
=lim x*sin1/x
=0
(sin1 / X is bounded and X tends to zero)

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