limx-0 ∫(sint+3t)dt/x^3= t属于[0,x]

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/22 19:40:00
limx-0∫(sint+3t)dt/x^3=t属于[0,x]limx-0∫(sint+3t)dt/x^3=t属于[0,x]limx-0∫(sint+3t)dt/x^3=t属于[0,x]lim(x→0

limx-0 ∫(sint+3t)dt/x^3= t属于[0,x]
limx-0 ∫(sint+3t)dt/x^3= t属于[0,x]

limx-0 ∫(sint+3t)dt/x^3= t属于[0,x]
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.