作者LuisSantos (^______^)
看板trans_math
标题Re: [极限]中兴95两题
时间Sat Jun 23 17:40:22 2007
※ 引述《osirisobelis (osirisNNN )》之铭言：
: 1.limX^1/x x->0+
: 2.lim(lnx)^x-1 x->1+
: 我2提答案都算1.不晓得有算的版友答案如何??
2. lim (lnx)^(x-1)
x→1+
= lim e^(ln((lnx)^(x-1)))
x→1+
= e^(lim ln((lnx)^(x-1)))
x→1+
= e^(lim (x-1)(ln(lnx)))
x→1+
ln(lnx)
= e^(lim ------------)
x→1+ (x-1)^(-1)
(1/(lnx))(1/x)
= e^(lim ------------------)
x→1+ (-1)((x-1)^(-2))
(-1)((x-1)^2)
= e^(lim ---------------)
x→1+ (x)(lnx)
(-1)(2)(x-1)
= e^(lim ----------------)
x→1+ lnx + (x)(1/x)
(-2)(x-1)
= e^(lim -----------)
x→1+ lnx + 1
0
= e^(-------) = e^0 = 1
0 + 1
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