微积分 求极限
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微积分 求极限
![](http://img.wesiedu.com/upload/0/8c/08c26c4f1c8851d9f8b1365faff84808.jpg)
![](http://img.wesiedu.com/upload/0/8c/08c26c4f1c8851d9f8b1365faff84808.jpg)
![微积分 求极限](/uploads/image/z/17078539-67-9.jpg?t=%E5%BE%AE%E7%A7%AF%E5%88%86+%E6%B1%82%E6%9E%81%E9%99%90+%26nbsp%3B)
两种方法:
原式=lim(x→0) [(x+e^x)/e^x*e^x]^(1/x)
=lim(x→0) [(1+x/e^x)*e^x]^(1/x)
=lim(x→0) (1+x/e^x)^(1/x)*(e^x)^(1/x)
=e*lim(x→0) (1+x/e^x)^(1/x)
=e*lim(x→0) (1+x/e^x)^[(e^x/x)*(1/e^x)]
=e*lim(x→0) [(1+x/e^x)^(e^x/x)]^(1/e^x)
=e*lim(x→0) e^(1/e^x)
=e*e^1
=e^2
原式=e^ln[lim(x→0) (x+e^x)^(1/x)]
=e^lim(x→0) ln(x+e^x)/x 【0/0型,洛必达法则】
=e^lim(x→0) (1+e^x)/(x+e^x)
=e^lim(x→0) (1+1)/(0+1)
=e^2
望采纳
再问: 谢谢 辛苦你了
原式=lim(x→0) [(x+e^x)/e^x*e^x]^(1/x)
=lim(x→0) [(1+x/e^x)*e^x]^(1/x)
=lim(x→0) (1+x/e^x)^(1/x)*(e^x)^(1/x)
=e*lim(x→0) (1+x/e^x)^(1/x)
=e*lim(x→0) (1+x/e^x)^[(e^x/x)*(1/e^x)]
=e*lim(x→0) [(1+x/e^x)^(e^x/x)]^(1/e^x)
=e*lim(x→0) e^(1/e^x)
=e*e^1
=e^2
原式=e^ln[lim(x→0) (x+e^x)^(1/x)]
=e^lim(x→0) ln(x+e^x)/x 【0/0型,洛必达法则】
=e^lim(x→0) (1+e^x)/(x+e^x)
=e^lim(x→0) (1+1)/(0+1)
=e^2
望采纳
再问: 谢谢 辛苦你了