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标题[试题] 100下 黄汉水 微积分乙下 第四次小考
时间Sat Jun 9 20:58:42 2012
课程名称︰微积分乙下
课程性质︰必修
课程教师︰黄汉水
开课学院：医学院
开课系所︰牙医、物治、职治、公卫、药学、医技、农化
考试日期（年月日）︰2012/06/07
考试时限（分钟）：17:30~18:40
是否需发放奖励金：yes
（如未明确表示，则不予发放）
试题 :
一、Let f(x,y,z)=(xyz)^1/2. Find the gradient and the maximum value of the
directional derivative of f(x,y,z) at the point (2,4,2). (25%)
二、Find the point on the graph of the equation 2x^2-y^2+z^2 = 1 at which the
normal line is parallel to the line passing through the points (-1,1,2)
and (3,3,3). (25%)
2 ┌ √(4-x^2) ┐
三、Find the integral ∫ │ ∫ e^(x^2+y^2) dy │ dx. (20%)
-2 └ 0 ┘
四、Let D be a lamina which is bounded by the curves y = sinx , y = 0 ,
x = 0 and x = π. If the density is den(x,y) = 12y the find the mass
and the center of mass of D. (30%)
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