※ 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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