※ 引述《ilovecurl (ilovecurl)》之銘言：
: http://www.lib.nccu.edu.tw/exam/transfer/math/index.htm
: 這個是政大應數考古題的網址
: 我要問的是92年微積分(一)的第3,6,7題
: 題目如下,看不清楚的可以去上面的網址看
: 3.the series
: ∞ cos(n^p) ∞ (lnn)^β cos(n^p)
: Σ ------------ and Σ --------------------
: n=2 n(lnn)^α n=2 n^α
: converge for every α>1,β>=1 and p>=1.
: 6.the following series is a rearrangement of the alternating harmonic
: series in which there appear alternately three positive terms followed
: by two negative terms
: 1 1 1 1 1 1 1 1 1
: 1 + --- + --- - --- - --- + --- + --- + ---- - --- - --- +++--...
: 3 5 2 4 7 9 11 6 8
: show that this series converges and has sum ln(√6).
: 7.for the sequence of functions f_n(x) = (x^2-1)^n.
: (3)
: define g_n(x) = f_n (x), n>=1. g_0(x) = 1.
: then prove or disprove g_n(x) converges uniformly in [0,√2].
這個第七題我會了,不過上面的兩題還是想不出來,有沒有好心的大大po一下詳解啊
另外同樣是這張的第4,5題問的題目,我不是很肯定他的意思
A farmer has 1000 feet of fence and wants to build a rectangular
enclosure along a straight wall.If the side along the wall needs no fence.
4.Find the dimensions that make the enclosure as large as possible.
5.Find the maximum area.
以下是我所理解的題意
wall
-------------------
x | | x
-------------------
1000-2x
上面的x是我自己假設的,然後求出最大的長方形面積和此時的長寬尺寸
不知道4.5題是不是這個意思,因為如果是,好像太簡單,感覺很奇怪,請各位幫個忙吧!
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