作者ptt789789 (昵称很难想>"<)
看板NTU-Exam
标题[试题] 94下 黄汉水 微积分甲下 期末考
时间Thu May 22 17:18:35 2008
课程名称︰微积分甲(下)
课程性质︰系定必修
课程教师︰黄汉水
开课学院:生机、生工、地质、工管
开课系所︰数学系
考试日期(年月日)︰2006/06/19
考试时限(分钟):170分钟
是否需发放奖励金:是
(如未明确表示,则不予发放)
试题 :
一 Find the equation of the tangent plane to the surface
xyz + (z^2)x - 2yz + 2 = 0 at the point (1,3,1). (20%)
二 Let D = { (x,y)│ x^2 + y^2 ≦ 45 } be a thin plate and the temperature
at the point (x.y) on the D is T(x,y) = 4xy + 3y^2
Find the highest and lowest temperatures. (20%)
三 Find the integral
4 1 1 2cos(x^2)
∫{∫[∫ ──────dx]dy}dz (20%)
1 0 y √z
四 Let D = { (x,y)│x^2 + (y-5)^2 ≦ 25 , x^2 + y^2 ≧ 25 } be a thin plate
1
Suppose the density at the point (x,y) is den(x,y) = ──────
√(x^2 + y^2)
Find the mass of D. (20%)
五 Let D be the region bounded by the curves y = 2x, y = 4x,
x = 2 and C = σD be the boundary of D.
Find the intergal ∮ (2xy - 3y)dx + x^2 dy. (20%)
c
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