Limx-0x6000-(sinx)6000/100.x2 (sinx)6000. Share with your friends Share 2 Anuradha Sharma answered this limx→0 x6000-sinx6000100x2sinx6000dividing by x6000 both in the numerator and denominator we get, limx→0 x6000-sinx6000x6000100x2sinx6000x6000=limx→0 1-sinxx6000100x2sinxx6000Now as we know that limx→0 sinxx=1 so putting limit we can see that is 00 so usingL'hospital rule we get, 1100limx→0 0-ddxsinxx6000ddxx2sinxx6000=1100limx→0-6000sinxx5999ddxsinxxx26000sinxx5999ddxsinxx+2xsinxx6000=1100limx→0-6000xcosx-sinxx26000x2xcosx-sinxx2+2xsinxx=1100limx→0-6000xcosx-sinxx26000xcosx-sinx+2sinx=1100limx→0-1x2+2x2sinx6000xcosx-sinxNow taking only limx→02x2sinxxcosx-sinx=limx→04xsinx+2x2cos x-xsinx+cosx-cosx=limx→04sinxx+2cos x-sinxx Dividing by x2 both in numerator and denominator=4+2-1=-6Now putting this value and limit value we get,1100limx→0-1x2+2x2sinxxcosx-sinx=1100×-10+-66000=10 13 View Full Answer Manu answered this it is x^2 -5
