作者victor7935 (victor)
看板trans_math
標題[微分] 求救求救...都是我的問題!??
時間Sun Nov 9 23:50:52 2008
1. Show that
x - (x^3)/6 < sinx for all x > 0
微1次後
f(x) = sinx -x + (1/6)x^3
f'(x)= cosx -1 + (1/2)x^2
然後.....
2.
Suppose that f is continuous on [a,b] and f(a)=f(b).
Show that f has at least one critical point in (a,b).
3.
(a)
Give an example of a nonconstant function that takes on both its
absolute max and absolute min on every interval.
(b)
Give an example of a nonconstant function that has an iinfinite
number of distinct local max and an infinite number of distinct
local min.
4.Use
1 - (1/2)x^2 < cosx < 1- (1/2)x^2 + (1/24)x^4 for all x>0.
to estimate cos 6度(the x above is in radians.)
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◆ From: 140.123.221.147
1F：→ Qmmm:1.x=0為C.P.,f(0)=0為 absolute minmum. 140.112.128.93 11/10 00:02
2F：→ Qmmm:f(0) < f(x) , for all x>0 140.112.128.93 11/10 00:02
3F：推 TaiwanFlight:1. let cosx=-1 then f'(x)=(1/2)x^2210.240.176.170 11/10 00:03
4F：→ TaiwanFlight:>0 for all x210.240.176.170 11/10 00:03
5F：→ TaiwanFlight:so f(x)遞增210.240.176.170 11/10 00:03
6F：→ Qmmm:2.少了f在(a,b)可微的條件 140.112.128.93 11/10 00:03
7F：→ TaiwanFlight:2. by Thm , true210.240.176.170 11/10 00:04
8F：→ TaiwanFlight:critical point是什麼點?210.240.176.170 11/10 00:05
9F：推 TaiwanFlight:2.f在[a,b]連續且f(x)=f(b)210.240.176.170 11/10 00:12
10F：→ TaiwanFlight:則f至少有一個臨界點在(a,b)210.240.176.170 11/10 00:12
11F：→ TaiwanFlight:f不需要可微210.240.176.170 11/10 00:13
12F：→ TaiwanFlight: f(a)210.240.176.170 11/10 00:13
13F：→ victor7935:那這樣是要有哪個定義證?!!140.123.221.147 11/10 00:17
14F：→ victor7935: 用140.123.221.147 11/10 00:19
※ 編輯: victor7935 來自: 140.123.221.147 (11/10 00:20)
15F：→ Qmmm: 2. 考慮f(x)=|x| ,f is cont. everywhere 140.112.128.93 11/10 00:21
16F：→ Qmmm:f(1)=f(-1) 但f在(-1,1)不可微 140.112.128.93 11/10 00:22
※ 編輯: victor7935 來自: 140.123.221.147 (11/10 00:22)
17F：推 TaiwanFlight:2. set f(x)=1 ,x no critical point210.240.176.170 11/10 00:25
18F：→ victor7935:所以不可微那點就是critical point!!140.123.221.147 11/10 00:27
19F：→ victor7935:是降嗎?140.123.221.147 11/10 00:27
20F：→ Qmmm:嗯嗯~~ 不存在點也是臨界點 抱歉忘了^^" 140.112.128.93 11/10 00:29
21F：→ victor7935:那就是分2種討論!? 1.可微..by MVT140.123.221.147 11/10 00:32
22F：→ victor7935:因為f(a)=f(b) ..f'(c)=0 ..2不可微.140.123.221.147 11/10 00:33
23F：→ victor7935:之點及是臨界點...這樣寫ok?140.123.221.147 11/10 00:33
24F：推 TaiwanFlight:3.(a) let f(x)=sin(x)210.240.176.170 11/10 00:46
25F：推 TaiwanFlight:3.(b) let f(x)=sec(x);(-pi/2,pi/2)210.240.176.170 11/10 00:51
26F：推 TaiwanFlight:4. x=0.104719667帶入210.240.176.170 11/10 00:53