求當x趨向於0時,函數(xarcsinxsin1/x)/sinx的極限

求當x趨向於0時,函數(xarcsinxsin1/x)/sinx的極限

(xarcsinxsin1/x)/sinx
=lim x/sinx *lim arcsinxsin1/x
=1*lim(arcsinx/x)*xsin1/x
=lim x*sin1/x
=0
(sin1/x有界而x趨於0)