已知f(x)在x=0处可导,且f(0)=0,则x趋近0时 lim(x^2f(x)-f(2x^3))/x^3=?
问题描述:
已知f(x)在x=0处可导,且f(0)=0,则x趋近0时 lim(x^2f(x)-f(2x^3))/x^3=?
答
x趋近0时 lim(x^2f(x)-f(2x^3))/x^3=lim(x->0)f(x)/x-lim(x->0)f(2x^3)/x^3=lim(x->0)[f(x)-f(0)]/x-lim(x->0)[f(2x^3)-f(0)]/x^3=f'(0)-2 lim(x->0)[f(2x^3)-f(0)]/2x^3=f'(0)-2f'(0)=-f'(0)lim(x->0)[f(x)-f(0)]/x=f'(0)����ô���ģ�