作者dreamingaway (Wherever I May Roam)
看板trans_math
标题[微积] 两题微积分
时间Thu Dec 30 18:59:10 2010
※ [本文转录自 Math 看板 #1D76MNSW ]
作者: dreamingaway (Wherever I May Roam) 看板: Math
标题: [微积] 两题微积分
时间: Thu Dec 30 18:57:24 2010
1. Define a function f:R→R by f(x)=0 if x belongs to R\Q,
and f(x)=1/p if x=q/p where p,q belong to Z, p≧1 and gcd{p,q}=1.
Show that lim f(x)=0
x→1/2
2. Let f,g:[0,1]→R, be continuous functions. Define h(x)=max{f(x),g(x)}
for all x belong to [0,1]. Show that h(x) is also a continuous function.
请问这2题要怎麽做 谢谢
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※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 218.168.124.231
1F：推 math1209:1.题目出的不好, 例如:x = 0 时, 没定义. 140.113.25.169 12/30 19:43
2F：→ math1209:一般来说都会在 0 点定义为 1. 然後用 140.113.25.169 12/30 19:43
3F：→ math1209:周期 "1" 来延拓出去. 140.113.25.169 12/30 19:44
4F：→ math1209:这一题:跟取的点 1/2 无关. 事实上, 140.113.25.169 12/30 19:44
5F：→ math1209:f(x) -> 0 if x -> c. c:任意实数. 140.113.25.169 12/30 19:45
6F：→ math1209:至於要怎麽做? 定义...想不出来就去查 140.113.25.169 12/30 19:45
7F：→ math1209:关键字: Riemann (popcorn) function. 140.113.25.169 12/30 19:46
8F：→ math1209:2. max (a,b) = ? 自己想想~ 140.113.25.169 12/30 19:46
9F：推 PaulErdos:可是它不是问x趋近1/2吗? 跟零点无定义 219.71.37.62 12/31 00:58
10F：→ PaulErdos:有何相干? 219.71.37.62 12/31 00:59
11F：→ PaulErdos:啊 我怎会用"零点"这词 我是说x=0 219.71.37.62 12/31 01:00
12F：推 math1209:因为题目出的是, f:|R -> |R =.= 140.113.25.169 12/31 01:08
13F：推 PaulErdos:.....原来是指那个 219.71.37.62 12/31 01:14
14F：推 math1209:因为题目出的好的话, 我们就有这结论: 140.113.25.169 12/31 16:40
15F：→ math1209:f(x) -> 0 if x -> c. c:任意实数. 140.113.25.169 12/31 16:40
16F：→ dreamingaway:第一题我查到了 61.224.231.31 12/31 16:47
17F：→ dreamingaway:第2题看不懂m大的提示@@ 61.224.231.31 12/31 16:47
18F：→ dreamingaway:不过还是谢啦 61.224.231.31 12/31 16:48