課程名稱︰微積分乙下
課程性質︰必修
課程教師︰黃漢水
開課學院：醫學院
開課系所︰牙醫、物治、職治、公衛、藥學、醫技、農化
考試日期（年月日）︰2012/06/07
考試時限（分鐘）：17:30~18:40
是否需發放獎勵金：yes
（如未明確表示，則不予發放）
試題 :
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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