lim(x→0) [∫(0→x) (sint + 3t) dt]/x³
= lim(x→0) (sinx + 3x)/(3x²),洛必达法则
= lim(x→0) (cosx + 3)/(6x),洛必达法则
= [cos(0) + 3]/(6(0)),分子不为0,所以要代入数值
= 4/0
= ±∞
此极限不存在.