课程名称︰微积分乙下 课程性质︰必修 课程教师︰黄汉水 开课学院：医学院 开课系所︰牙医、物治、职治、公卫、农化、医技、药学 考试日期（年月日）︰2012/05/01 考试时限（分钟）：120min. 是否需发放奖励金：yes （如未明确表示，则不予发放） 试题 : 一、Find the following integrals: (30%) 3 x+2 (1)∫ --------------------- dx 1 x^4 + x^3 + x^2 + x π/2 cosx (2)∫ ------------ dx π/3 1 + cosx e^π (3)∫ cos(lnt)dt 1 二、Find the volume of the solid obtained by revolving the region under the graph of y = e^(-x) on [0,∞) about x-axis. (15%) 三、Find the radius of convergence and the interval of convergence of the following power series. (20%) +∞ x^n (1)Σ -------------- n=2 (3^n)n(ln n)^2 +∞ 1 (2)Σ ------------------ x^n n=1 2‧5‧8 … (3n-1) 四、Find the Taylor series of the function f(x)= cos^2(x) at the given value c=0. (15%) +∞ 1 五、Let h(x)= Σ -------- x^(n+1) for any ∣x∣< 1. (20%) n=1 n(n+1) Find the function h(x) and the values h(0,4), h'(0,3). --

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