如图!能大概说一下解题过程最好了...
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如图!
能大概说一下解题过程最好了...
![](http://img.wesiedu.com/upload/2/c1/2c1a08848d4db0d4ecca318806fb3b34.jpg)
能大概说一下解题过程最好了...
![](http://img.wesiedu.com/upload/2/c1/2c1a08848d4db0d4ecca318806fb3b34.jpg)
![如图!能大概说一下解题过程最好了...](/uploads/image/z/16324574-14-4.jpg?t=%E5%A6%82%E5%9B%BE%21%E8%83%BD%E5%A4%A7%E6%A6%82%E8%AF%B4%E4%B8%80%E4%B8%8B%E8%A7%A3%E9%A2%98%E8%BF%87%E7%A8%8B%E6%9C%80%E5%A5%BD%E4%BA%86...)
1.
极限可化为
lim [x(1+ln(1+x)/x)]/[x(2-ln(1+x)/x)]
=lim (1+ln(1+x)/x)/(2-ln(1+x)/x)
lim ln(1+x)/x=lim x/x=1,得
lim (1+ln(1+x)/x)/(2-ln(1+x)/x)=1/2
2.
e^(πx)-1πx,极限可化为
lim (π/2x)*[1/2-1/(e^(πx)-1)]
=lim (π/2x)*[(e^x-3)/2(e^x-1)]
=lim (π/2x)*[(e^x-3)/2x]
=lim [π(e^x-3)]/[4x^2]
x→0,e^x→1,x^2→0且大于0
所以极限等于-∞
极限可化为
lim [x(1+ln(1+x)/x)]/[x(2-ln(1+x)/x)]
=lim (1+ln(1+x)/x)/(2-ln(1+x)/x)
lim ln(1+x)/x=lim x/x=1,得
lim (1+ln(1+x)/x)/(2-ln(1+x)/x)=1/2
2.
e^(πx)-1πx,极限可化为
lim (π/2x)*[1/2-1/(e^(πx)-1)]
=lim (π/2x)*[(e^x-3)/2(e^x-1)]
=lim (π/2x)*[(e^x-3)/2x]
=lim [π(e^x-3)]/[4x^2]
x→0,e^x→1,x^2→0且大于0
所以极限等于-∞