作者ptt789789 (昵称很难想>"<)
看板NTU-Exam
标题[试题] 96下 黄汉水 微积分甲下 期末考
时间Mon Jun 16 22:39:34 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)︰2008/06/15
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
(e^x)yz + 3(z^2) - 2(y^2)z - 10 = 0 at the point (0,1,2) (15%)
二 Let D = {(x,y,z)︱x^2 + y^2 + z^2 ≦ 50 } be a thin plane and
the temperature at the point (x,y,z) on the D is
T(x,y,z) = 9(x^2) + 9(y^2) + 9(z^2) + 6xy + 8yz
Find the highest and lowest temperatures (25%)
2 4 _______
三 Find the integral ∫[∫ 6x√y^2 + 9 dy]dx (15%)
0 x^2
四 Let D = {(x,y)︱(x-2)^2 + y^2 ≦ 4 , y≦0 } be a thin plane (20%)
Suppose that the density at the point (x,y) is den(x,y) = -12y
(1) Find the mass of D
(2) Find the center of mass of D
五 Let D = {(x,y,z)︱x^2 + y^2 + z^2 ≦ 25 , z≧3 } Suppose that the
density at the point (x,y,z) is den(x,y,z) = 12z
Find the mass of D (15%)
六 Let D = {(x,y)︱x^2 + y^2 ≦ 16 , y≧0 } and C = σD be the bound of D
Find the intergal ∫(2xy + 3x)dx + (x^2 + 2x)dy (10%)
c
--
※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 118.165.108.21