lim{x->0} (1/x) ∫[0, 1] f(xt) dt
= ∫[0, 1] t*lim{xt->0}{f(xt)-f(0)}/(xt) dt
= ∫[0, 1] t*f'(0) dt,注意：lim{xt->0}{f(xt)-f(0)}/(xt) = f'(0)
= f'(0)(0.5t^2) from 0 to 1
= 0.5f'(0)
美国高中数学老师