Re: [高微] 連續,Compactness,偏微 方面的問題

[TrySoHard (夢永遠都只是夢)]

提供你一點想法


1. Let  f(x) = x  if x is rational , f(x) = 0  if x is irrational.
Show that  f  is continuous at  x = 0  and nowhere else.

這題用continuous的定義應該就可以做了


2. Show that an infinite set S 包含於 R^n(空間) is compact if and only if
every
infinite subset of S has an accumulation point that lies in S.

利用:Heine-Borel Theorem ~
      A set S in R^n is compact iff it is closed and bounded.

還有:Bolzano-Weierstrass Property


3. If u = x^2 + 3*y^2 and y = x*z , there are two possible meanings for  ∂u/
∂x  depending on whether the independent variables are taken as (x , y) or
(x, z) .
Compute both them.


註：第3題的 "∂" 是偏微(partial)的符號。


--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 163.14.7.117
→ ntust661    :看不到Partial!
--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 140.114.203.52
推 rockdancer  :謝謝你的建議~我試試看XD可以順便問一下第3題，是直
→ rockdancer  :接對U做X的偏微的計算就可以了嗎?
→ TrySoHard   :應該是吧
→ TrySoHard   :拍謝...我很懶  所以只給你想法
推 rockdancer  :我寫了但第2題我老師說我寫錯了= =