→ k87:我又慢了 > < 140.115.202.63 04/24 11:41
→ sioumi:XD 初微解題競爭好激烈 59.113.55.105 04/24 11:41
※ 編輯: k87 來自: 140.115.202.63 (04/24 11:48)
※ 引述《king911015 (早已放棄愛上你)》之銘言：
: 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
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.115.202.63