Re: [積分] 極限
※ 引述《olala313 (喔耶耶)》之銘言：
: 1 x 2
: lim -----∫ cos t dt
: x→0 x 0
: 1 2 0
: = lim -----* sin x (-----)
: x→0 x 0
: 2
: = lim cos x * 2x
: x→0
: =0
: 想請問這樣做對嗎?
1 x 2
lim -----∫ cos t dt
x→0 x 0
d x 2
--- lim ∫ cos t dt
dx x→0 0
= ----------------------
d
--- lim x
dx x→0
2
= lim ( cos x ) * 1
x→0
=1
btw.這題是因為上限對x微是1,下限是0
所以看起來像是直接代入,
要是上限是g1(x),則最後一行要改成f(g1(x))*g1'(x)
下限要是不幸也是x的函數g2(x),
則改成f(g1(x))*g1'(x)) - f(g2(x))*g2'(x)
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 218.170.57.138
推
12/15 18:14, , 1F
12/15 18:14, 1F
→
12/15 23:25, , 2F
12/15 23:25, 2F
推
12/16 08:58, , 3F
12/16 08:58, 3F
→
12/16 18:45, , 4F
12/16 18:45, 4F
→
12/17 00:14, , 5F
12/17 00:14, 5F
→
12/17 00:14, , 6F
12/17 00:14, 6F
→
12/24 01:24, , 7F
12/24 01:24, 7F
→
12/24 01:30, , 8F
12/24 01:30, 8F
→
12/24 01:31, , 9F
12/24 01:31, 9F
→
12/24 01:32, , 10F
12/24 01:32, 10F
→
12/24 01:38, , 11F
12/24 01:38, 11F
→
12/24 01:39, , 12F
12/24 01:39, 12F
→
12/24 01:39, , 13F
12/24 01:39, 13F
→
12/24 01:42, , 14F
12/24 01:42, 14F
→
12/24 01:43, , 15F
12/24 01:43, 15F
→
12/24 01:51, , 16F
12/24 01:51, 16F
→
12/24 01:52, , 17F
12/24 01:52, 17F
→
12/24 01:52, , 18F
12/24 01:52, 18F
→
12/24 01:54, , 19F
12/24 01:54, 19F
→
12/24 01:54, , 20F
12/24 01:54, 20F
→
12/24 01:59, , 21F
12/24 01:59, 21F
討論串 (同標題文章)