作者himawarigirl (请登入‧线实)
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标题[试题] 96下 王蔼农 微积分乙下 期中考
时间Fri Apr 18 02:10:29 2008
课程名称︰微积分乙下
课程性质︰必修
课程教师︰王蔼农
开课学院:理学院
开课系所︰数学系
考试日期(年月日)︰08/04/17
考试时限(分钟):110分钟
是否需发放奖励金:是
(如未明确表示,则不予发放)
试题 :
(满分40)(4 for each)
1.
Power series 2*4*6*...*(2n)
Σ ──────── x^n
1*3*5*...*(2n+1)
radius of convergence r =?
domain of convergence -r<(=)x<(=)r?
2.
f(x)= e^(x^2)
(12)
f (0)=?
3.
∞
Σ ㏑(1-1/n^2)=?
n=2
4.
cardioid r=1+sinθ arclength=?
5.
r≦3sinθ , r≧2-sinθ area=?
6.
Parallelepiped with vertices (0,0,0),(3,0,0),(0,5,1),(3,5,1),
(2,0,5),(5,0,5),(2,5,6),(5,5,6)
volume = ?
7.
某地 60°N,30°E 杭州 30°N,120°E distance=?
Hint: radius of the earth r = 40,000÷2π km sin60°=√3/2
8.
L1= X/3=(Y-2)/(-1)=Z+1
L2= (X-1)/4=Y+2=(Z+3)/(-3)
distance=?
9.
→ →
r (t)=(t,t^2,t^3/3) t=1 bi-normal vector B = (?,?,?)
10.
→
r (t)=(5cost,4sint) t=π/2
center of curvature= (?,?)
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