課程名稱︰微積分乙下
課程性質︰
課程教師︰張秀瑜
開課系所︰管理學院
考試時間︰2005.04.21
試題 :
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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