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标题[转录][试题] 93下 张秀瑜 微乙 期中考题
时间Sat Feb 23 13:56:45 2008
※ [本文转录自 NTU-Exam 看板]
作者: cawaiik (5/1台大热舞成发在旧体) 看板: NTU-Exam
标题: [试题] 93下 张秀瑜 微乙 期中考题
时间: Fri Apr 22 01:18:12 2005
课程名称︰微积分乙下
课程性质︰
课程教师︰张秀瑜
开课系所︰管理学院
考试时间︰2005.04.21
试题 :
1. Solve the equation du/dt = 2t = (sec t)^2 / 2u , u(0) = 1
2. Find the length of the polar curve r = θ^2 , 0≦θ≦2π
3. (a) Find a Cartesian equation for the curve r = 4sinθ
(b) Find the area of the region that lies inside r = 4sinθ
and outside r = 2
4. x = 1 + t^2 , y = t - t^3 . Find dy/dx and (dy)^2/(dx)^2
5. Determine the following is convergent or divergent .
(1) an = (-3)^n / n!
∞ -x^2
(2) ∫ x e dx
0
∞ -n^2
(3) Sigma n e
i = 1
6. Find the radius of convergence and interval of convergence of
∞
the series Sigma (-1)^n (x+2)^n / n 2^n
n = 1
7. Find the Maclaurin series and the radius of convergence for
the following functions :
(1) f(x) = ln (1+x)
(2) f(x) = x sinx
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