※ 引述《venwhah (昆)》之銘言： : 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 G(x,y,z,λ) = x+3y-2z + λ(x^2 + y^2 +z^2 =14) Gx = 1 + 2λx = 0..................同乘yz Gy = 3 + 2λy = 0..................同乘xz Gz = -2 + 2λz = 0.................同乘xy 得 -2λxyz = yz = 3xz = -2xy.........得 y = 3x = (-3/2)z 代回原條件 (x,y,z) = (1,3,-2).............. 14.....max = (-1,-3,2)............. -14.....min 各位有考成大的高手 是算這個答案嗎? 有錯請指正! : 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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