Re: [考古] 高大95年
※ 引述《TACO0526 (我很好)》之銘言:
: 到仿間書局找過了,找不到答案
: 所以把題目po上來,麻煩大家幫我解題
: 如果有能力一次解下面10題者,可來信報價錢
: (會先提供一些有解答的題目,做測試,看是否確實有能力)
: 或者有95高大詳解者,也可直接來信報價
: ∞
: 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)
(3)(u^2 + 3v) - (2u)(3u - 2v)
fu = -------------------------------
(u^2 + 3v)^2
(-3)(u^2) + 4uv + 9v
= ----------------------
(u^2 + 3v)^2
(-2)(u^2 + 3v) - (3)(3u - 2v)
fv = -------------------------------
(u^2 + 3v)^2
(-2)(u^2) - 9u
= ----------------
(u^2 + 3v)^2
: (b)g(x,y)=(x+2)^2(y+3)^3
gx = (2)(x+2)((y+3)^3)
gy = ((x+2)^2)((3)((y+2)^2)) = (3)((x+2)^2)((y+2)^2)
: 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.
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