Re: [積分] 請問這兩題如何計算?
※ 引述《flygey (努力達成目標)》之銘言：
: 1.判別下列瑕積分及無窮級數為收斂還是發散
: +∞
: ∫ 1/((lnx)^x)
: 2
: ∞
: ---
: \
: / 1/((lnK)^K)
: ---
: K=2
: 2. 2x -1
: f(x)=∫ (16+t^4)^(1/2)dt find (f )'(0)
: 1
: 可以教我嗎 感謝
: ※ 編輯: flygey 來自: 59.112.184.105 (05/24 20:55)
-1
2. 令 g = f , 則 g(f(x)) = x
(g'(f(x)))(f'(x)) = 1
1
g'(f(x)) = -------
f'(x)
2x
f(x) = ∫ (16 + t^4)^(1/2) dt
1
1
令 f(x) = 0 , 則 2x = 1 => x = ---
2
f'(x) = (2)((16 + (2x)^4)^(1/2))
f'(1/2) = (2)((16 + ((2)(1/2))^4)^(1/2))
= (2)((16 + 1^4)^(1/2))
= (2)((16 + 1)^(1/2))
= (2)((17)^(1/2))
-1 1 1
(f )'(0) = --------- = -----------------
f'(1/2) (2)((17)^(1/2))
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 61.66.173.21
推
05/25 00:58, , 1F
05/25 00:58, 1F
討論串 (同標題文章)