cotx(1/sinx-1/x)x趋向于0的极限

问题描述:

cotx(1/sinx-1/x)x趋向于0的极限

=lim(cotx)(1/sinx-1/x) =lim(cotx)(x-sinx)/(xsinx) =lim[cosx(x-sinx)/x(sinx)^2] =lim[(xcos-(sin2x)/2)/x^3],洛必达法则 =lim[(cosx-xsinx-cos2x)/3x^2],洛必达法则 =lim[(2sin2x-2sinx-xcosx)/6x] =2/3-1/3-1/6...