※ 引述《TACO0526 (我很好)》之铭言： : 到仿间书局找过了，找不到答案 : 所以把题目po上来，麻烦大家帮我解题 : 如果有能力一次解下面10题者，可来信报价钱 : (会先提供一些有解答的题目，做测试，看是否确实有能力) : 或者有95高大详解者，也可直接来信报价 : ∞ : 1.∫ (1/x)dx : 1 : 1 : 2.∫ (1/x^3)dx : -1 : ∞ : 3.∫ (1/x^2)dx : 1 : 4.Find the partial derivatives forthe following function. : (a)f(u，v)=(3u-2v)/(u^2+3v) : (b)g(x，y)=(x+2)^2(y+3)^3 : 5.Find the total derivative of the following function. : (a)y=f(x，w)，where x=g(w) : (b)y=f(c，s)，where s=g(c) : (c)y=f(x1，x2，w)，where x1=g(w) and x2=h(w) : (d)y=f(K，L，u，v)，where K=g(u，v) and L=h(u，v) : 6.Find the derivative of the following function. : (a)t^3*lnt^2 : (b)x^a*e^kx-c : 7.Find dz and dz^2 of the following function. : (a)z=f(x，y) : (b)z=f(x，y，w) : 8.Check z=x^2+y^2 for convexity or concavity by the derivative conditions. : 9.Finf the extremes value(s) of z=2x^2+xy+4y^2+xw+w^2+2. : 10.Using the Lagrange-multiplier method and find the extremum of z=x^2+y^2 : subject to x+4y=2. 10. 令 z = f(x,y) = x^2 + y^2 g(x,y) = x + 4y - 2 F(x,y) = f(x,y) + (λ)(g(x,y)) = x^2 + y^2 + (λ)(x + 4y - 2) Fx = 2x + λ = 0 => λ = -2x => y = 4x 代入x + 4y = 2 Fy = 2y + 4λ = 0 => λ = -y/2 x + 16x = 2 => 17x = 2 => x = 2/17 => y = 4x = 8/17 当(x,y) = (2/17 , 8/17) 时 , z = f(2/17 , 8/17) 4 64 68 4 = ----- + ----- = ----- = ---- 为极大值 289 289 289 17 --

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