作者k87 (谁不希望天长地久)
看板trans_math
标题Re: [积分]
时间Tue Apr 24 11:40:44 2007
※ 引述《king911015 (早已放弃爱上你)》之铭言：
: 1 x
: Evaluate lim --- ∫ (1 - tan2t)^1/t dt
: x→0 X 0
1 x
lim --- ∫ (1 - tan2t)^1/t dt
x→0 x 0
x
∫ (1 - tan2t)^1/t dt
0
= lim ------------------------
x→0 x
(1 - tan2x)^1/x
= lim --------------------
x→0 1
1
- ln (1 - tan2x)
x
= lim e
x→0
1
lim - ln (1 - tan2x)
x→0 x 1
= e lim - ln (1 - tan2x)
x→0 x
-2
= e -2(sec 2x)^2
= lim --------------
x→0 1 - tan2x
= -2
--
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