课程名称︰微积分甲下
课程性质︰大一必修
课程教师︰容志辉
开课学院：工学院
开课系所︰电机系、材料系
考试日期（年月日）︰2015/4/20
考试时限（分钟）：50分 钟
试题 :
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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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