23/06/13 18:45:45.87 z+SivvI1.net
g(x)=sinx-x+x^3/6=g(x)-g(0)=xg'(t)
=x(cost-1+t^2/2)=xt(cosu-1+u^2/2)'=xt(-sinu+u)=xtu(-sinv+v)'
=xtu(-cosv+1)=-2xtu(sin(v/2))^2 0<v<u<t<x
(x^3-g(x))/x^3→1(x→0)
23/06/13 18:45:45.87 z+SivvI1.net
g(x)=sinx-x+x^3/6=g(x)-g(0)=xg'(t)
=x(cost-1+t^2/2)=xt(cosu-1+u^2/2)'=xt(-sinu+u)=xtu(-sinv+v)'
=xtu(-cosv+1)=-2xtu(sin(v/2))^2 0<v<u<t<x
(x^3-g(x))/x^3→1(x→0)