f(x)具有二阶连续导数,且f(0)=f'(0)=0,f''(x)>0,u(x)是y=f(x)在点(x,f(x))处的切

x0处切线为y=f(x0)+f'(x0)(x-x0)
所以u(x0)=x0-f(x0)/f'(x0)
即u(x)=x-f(x)/f'(x)
所以lim(x→0)x/u(x)
=lim(x→0)xf'(x)/(xf'(x)-f(x))
=lim(x→0)(f'(x)+xf''(x))/(f'(x)+xf''(x)-f'(x)) （洛必达法则）
=lim(x→0)(f'(x)+xf''(x))/(xf''(x))
=lim(x→0)(f'(x)/x+f''(x))/f''(x)
=lim(x→0)[(f'(x)-f'(0))/(x-0)+f''(x)]/f''(x)
=(f''(0)+f''(0))/f''(0)
=2