[試題] 97上 微積分乙 王振男 期末考
課程名稱︰微積分乙
課程性質︰系必帶
課程教師︰王振男
開課學院：醫學院
開課系所︰醫學系
考試日期（年月日）︰12/13
考試時限（分鐘）：140min
1.判斷以下命題，如為真須證明、否則需舉反例
(a) ΣAn converges absolutely => ΣAn^2 converges
(b) ΣAn^2 converges => ΣAn converges absolutely
(c) ΣAn converges => ΣAn^2 converges
2.判斷以下級數是否收斂，需註明以何種方式檢驗
(a)Σ(-1)^(n+1)*sin(π/n)
(b)Σ(-1)^(n+1)*nsin(π/n)
(c)Σ1/(㏑n)^p , for all p > 1
3.決定此瑕積分是否收斂，如收斂需計算其值
1
∫ (㏑(1/x))^2 dx
0
(hint: set t = ㏑(1/x))
4.
x^3
∫──── dx
√(1-x^2)
5.
∫x㏑(x+2)dx
6. A 200-gal tank is half full of distilled water. At time t=0, a solution
containing 0.5 pound/gal of concentrate enters the tank at the rate of
5gal/min, and the well-strred mixture is withdrawn at the rate of 3gal/min
a. At what time will the tank be full?
b. At the time the tank is full, how many pounds of concentrate will it
contain?
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01/17 01:34, , 1F
01/17 01:34, 1F