课程名称︰微积分甲上 课程性质︰大一必修 课程教师︰朱桦 开课学院：工学院 开课系所︰材料系、电机系 考试日期（年月日）︰2014/12/1 考试时限（分钟）：20min 试题 : CALCULUS QUIZ 4 Instructor: Professor Huah Chu Quiz date: Dec. 1, 2014 Quiz time: 20 minutes Total score: 20 points (5 points for each problem) ======================================================================== 1. Find the limit n k*n^2 lim Σ -------------- n→∞k=1 (n^2+k^2)^2 2. Suppose f' is continuous on [a,b]. For any x ∈(a,b), under what conditions d x x --- ∫f(t)dt = ∫f'(t)dt ? (You have to write down the reasons) dx a a 3. Evaluate the indefinite intergral tan^3(x) dx ∫-------------- sec^(1/3)(x) 4. Evaluate the indefinite intergral ∫sin(x^(1/3)) dx --

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