lim(x→0)=(arctanx-x)/ln(1+2x^3)

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/23 09:43:24
lim(x→0)=(arctanx-x)/ln(1+2x^3)lim(x→0)=(arctanx-x)/ln(1+2x^3)lim(x→0)=(arctanx-x)/ln(1+2x^3)说明:此题书写

lim(x→0)=(arctanx-x)/ln(1+2x^3)
lim(x→0)=(arctanx-x)/ln(1+2x^3)

lim(x→0)=(arctanx-x)/ln(1+2x^3)
说明:此题书写错误,应该是“lim(x→0)[(arctanx-x)/ln(1+2x^3)]”.
原式=lim(x->0)[(arctanx-x)'/(ln(1+2x^3))'] (0/0型极限,应用罗比达法则)
=lim(x->0)[-(1+2x^3)/(6(1+x^2))]
=-(1+0)/(6(1+0))
=-1/6.