課程名稱︰微積分甲下
課程性質︰大一必修
課程教師︰容志輝
開課學院：工學院
開課系所︰電機系、材料系
考試日期（年月日）︰2015/4/20
考試時限（分鐘）：50分 鐘
試題 :
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Calculus 02 Quiz 2
1. Let f(x,y) = 2 2
x + 2y
───── , (x,y) ≠ (0,0)
x + y
0, (x,y) ＝ (0,0)
(a) Find fx(0,0) and fy(0,0).
(b) Are the two partial derivative continuous at (0,0)? Give your
explanation.
2. Use Lagrange's multiplier method to find the maximum and the minimum of
2 2
g(x,y,z) = x + y + z when the constraints are x + y = 4 and x - y + z = 1.
4 2 2 4 2 2
3. Find the extreme value of f(x,y) = x + 2x y + y + 2x - 4xy + 2y + 1.
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