[考古] 今年的成大考題 @@
以下是今年的成大微積分部分考題
只有抄這幾提出來 (唉 變炮灰 囧 )
大概是看中文的題目慣了 有些都不會算
一整個不知道該說什麼
有會的人就幫忙解一下吧
非常感謝
1.Use the method of Lagrange Multiplier to find the max value of the fuction
3 2 2 2
f(x,y,z)=x+3y-2z define on R subject to the constrain x + y +z =14
2.Let f be a real valued fuction defined on R with f"(x)>0
for all x ,show that f(x)≧f'(0)+f(0) for all x
3. x
e ㏑(x+e) 1
Let f(x)=∫ ---------------- dx defined on (-1,∞)
1 4 2
√(x + x +5)
(a)show that f is a strictly increasing fuction
-1
(b)find (f )'(0)
4. 1 n 3i 7 3i 4
lim --- Σ √(-----) +(-----)
n->∞ n i=1 n n
5.Find area of the region Ω bounded by the curve
2 2 2
x -4xy+4y -2x-y-1=0 and y =---
5
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