紧急:求lim tan(e^(x-1)-e^(x^2-1))/(arctanx-π/4),X趋于1;

2个回答

  • 利用等价无穷小和罗比达法则.

    e^(x-1)-e^(x^2-1)趋于0,tanx与x等价.又因为分子,分母都趋于0,可以用罗比达法则.

    如下

    lim tan(e^(x-1)-e^(x^2-1))/(arctanx-π/4)=(e^(x-1)-e^(x^2-1))/(arctanx-π/4)=(e^(x-1)-2xe^(x^2-1))(1+x^2)

    然后将x=1代入得

    lim tan(e^(x-1)-e^(x^2-1))/(arctanx-π/4)=(e^(x-1)-e^(x^2-1))/(arctanx-π/4)=(e^(x-1)-2xe^(x^2-1))(1+x^2)=-2