『漫游』酷论坛>『海外生活』>来，看看这道题目
aaabbbccc@2003-12-10 15:02
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最初由 sigmond 发布
这个应该是高中学生就可以做的吧
偶也来一个，偶只知道答案，不会做
从-无穷到+无穷的 exp（-t*t/2）dt的积分
答案是 （2*PI）^（1/2）
求过程
r u sure? as i write, anything smaller than 3 is not the answer.
in this question, 3 and 1% will affect the answer greatly. without count them in, u will just get zero marks
BTW, just my wild guess, the real thing matter's here is e. the natural log base.
tBlue@2003-12-10 15:07
是不是要列一个方程式，然后求极限值啊，这只是一个思路哦
pojen@2003-12-11 00:13
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最初由 sigmond 发布
自乘一次轉 polar？？什么意思
这是个偶函数 我知道啊，就是2*从0到+无穷的 exp（-t*t/2）dt的积分
过程是什么？ exp（-t*t/2）dt的原函数是什么？
sorry..... can't type Chinese........
solution = sqrt(Int (exp(-x^2 / 2) * exp(-y^2 / 2) dxdy))
in polar system, x^2 + y^2 = r^2
=> Solution = sqrt(Int (exp(-r^2 / 2) rdrd theta))
sigmond@2003-12-11 02:33
d theta 是 dθ 对吧
我明白了。 Int (exp(-r^2 / 2) rdr 从0到+无穷 ＝ 1
Int (d theta) 从0到2π ＝ 2π
然后就是答案了
楼上的真强啊～～～
请问你是大学几年纪啊。因为我还没有学到把积分自乘 然后转换到解析几何，这个思路实在巧妙。
sigmond@2003-12-11 02:35
求极限值是必然的 因为无穷是不能用来定积分的，只能先积分再求极限
谢谢你帮助啦
seiyafan@2003-12-11 05:56
我觉得答案是应该和存钱的总天数有关系的，所以此题没有一个固定的答案。
aaabbbccc@2003-12-11 12:25
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最初由 seiyafan 发布
我觉得答案是应该和存钱的总天数有关系的，所以此题没有一个固定的答案。
with a long enough time, the winner will emerge clearly with ur question though. it's surely not a fixed number for different precondition, that's why i think ppl give out a number without even consider the precondition funny.
regardless to whatever precondition, i think e, the most efficient number in the universe, is the essential part of the answer as this whole thing is n/N >=logf(n)/logf(N). visually, it's a log curve always below a straight line.(the differential may not be)
macrossjing@2004-01-08 08:51
看了半天！！答案：应该是无解。
Lizard@2004-01-08 13:26
holy...optimization problem..
i can't solve it!! itz too hard..
ambivalence@2004-01-16 01:48
引用
最初由 aaabbbccc 发布
with a long enough time, the winner will emerge clearly with ur question though. it's surely not a fixed number for different precondition, that's why i think ppl give out a number without even consider the precondition funny.
regardless to whatever precondition, i think e, the most efficient number in the universe, is the essential part of the answer as this whole thing is n/N >=logf(n)/logf(N). visually, it's a log curve always below a straight line.(the differential may not be)
I don't understand where the n/N >= log f(n) / log f(N) comes from. Also why is e the most efficient number? efficient in what sense? I haven't studied maths for a while, so forgive me if I'm asking silly questions.
All I managed to get is 100000*(1+(m-3))^(n/m) = amout at maturity. Where can I go from there
大太阳@2004-01-17 04:55
我想应该是14天一次啊。
aaabbbccc@2004-01-17 11:55
引用
最初由 ambivalence 发布
I don't understand where the n/N >= log f(n) / log f(N) comes from. Also why is e the most efficient number? efficient in what sense? I haven't studied maths for a while, so forgive me if I'm asking silly questions.
All I managed to get is 100000*(1+(m-3))^(n/m) = amout at maturity. Where can I go from there
faint, this problem seems keep come to the surface and refuses to die.
if u take n*N days, u will get that equation. if N is the answer then f(n)^N<=f(N)^n , f(x) is the equation for 1 round with x days. and the initial value doesnt really matter here unless the bank has some charge per day.
btw, this whole thing is a variation of n/N >=log(n)/log(N) and the answer for that is N=e. (1/N is the derivative of log(n)/log(N) when n==N, it can be seen more clearly on a graph)
e is the most efficient number is refering to if a number system is base e, u will need minimun symbols(states) to store a number in general (it's actrually the same problem as the one above). in computer, it means base 3 is most efficient for storing data, base 2 is not that bad also. anything else will waste a lot of states in general.
ambivalence@2004-01-18 04:27
ok, I won't pretend I've understood what you said, because I haven't. I'll just take your word for it ;-)
杜诗@2004-01-18 12:52
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最初由 ThunderBird 发布
做不来
真的有答案吗？好象无解的说。
ibic@2004-01-19 20:00
好像不是很难，，，，but我做不出来。
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