课程名称︰微积分乙 课程性质︰系必带 课程教师︰王振男 开课学院：医学院 开课系所︰医学系 考试日期（年月日）︰12/13 考试时限（分钟）：140min 1.判断以下命题，如为真须证明、否则需举反例 (a) ΣAn converges absolutely => ΣAn^2 converges (b) ΣAn^2 converges => ΣAn converges absolutely (c) ΣAn converges => ΣAn^2 converges 2.判断以下级数是否收敛，需注明以何种方式检验 (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.决定此瑕积分是否收敛，如收敛需计算其值 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containing 0.5 pound/gal of concentrate enters the tank at the rate of 5gal/min, and the well-strred mixture is withdrawn at the rate of 3gal/min a. At what time will the tank be full?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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