lim(ⅹ-1)e^π/2+arctanx-e^πⅹ
答案:2 悬赏:30 手机版
解决时间 2021-02-02 05:41
- 提问者网友：容嬷嬷拿针来
- 2021-02-01 05:14
lim(ⅹ-1)e^π/2+arctanx-e^πⅹ
最佳答案
- 五星知识达人网友：鱼忧
- 2021-02-01 05:40
lim(x→∞) (2/π*arctanx)^x
=e^lim(x→∞) xln(2/π*arctanx)
=e^lim(x→∞) ln(2/π*arctanx)/(1/x)
用洛必达法则得
=e^lim(x→∞) 1/[(x^2+1)arctanx]/(-1/x^2)
=e^-lim(x→∞) x^2/[(x^2+1)arctanx]
=e^-lim(x→∞) x^2/(x^2*arctanx+arctanx)
=e^-lim(x→∞) 1/[arctanx+(arctanx)/x^2],取得极限
=e^-1/(π/2+0)
=e^(-2/π)
=e^lim(x→∞) xln(2/π*arctanx)
=e^lim(x→∞) ln(2/π*arctanx)/(1/x)
用洛必达法则得
=e^lim(x→∞) 1/[(x^2+1)arctanx]/(-1/x^2)
=e^-lim(x→∞) x^2/[(x^2+1)arctanx]
=e^-lim(x→∞) x^2/(x^2*arctanx+arctanx)
=e^-lim(x→∞) 1/[arctanx+(arctanx)/x^2],取得极限
=e^-1/(π/2+0)
=e^(-2/π)
全部回答
- 1楼网友：话散在刀尖上
- 2021-02-01 06:36
不明白啊 = =！
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