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Claim: Let E be measurable set of |R^2, Suppose for almost...,{x:(x,y)€E} has measure zero Now let E={(x,y)€|R^2:f(x,y)=+∞},then for almost every...

F=(x,y,z), divF=1+1+1=3 Let S be the boundary of the region R(volume of R is V...

...;=> A is invertible 註: onto的說明 For any y in R^n, is there x in R^n, such that G(x)=y. i.e. c...

Claim: K is a ring. Proof: Let A and B be sets in K. There are collections {A1, A2...

|S9| = 9! = 2^7 * 3^4 * 5 * 7 Let H = <(1,2,3),(4,5,6),(7,8,9)> ,sigma=(1,4...5,8)(3,6,9)> } And there are 36 9-cycles in S9 ---> N3 = 8!/36 = 1120

Let An = { T(i) + S(i) : i is integer and i ≧ n } Bn = { T(i) : i is... limit on both sides, it means lim inf An ≧ lim inf Bn + lim inf Cn. 2. Let S(n)=(-1)^n, T(n)=(-1)^(n+1). We have S(n)+T(n)=0 for all n. Moreover...

...you mean -2xy sin(x^2) dx + cos(x^2)dy = 0 ? sin(x^2)d(x^2)=cos(x^2)dy/y let X=x^2 tan(X)dX=dy/y .... Now its your...

(∂h/∂x, ∂h/∂y, ∂h/∂z)≠(0,0,0) 不失一般性,可設∂h/∂z ≠0 因 h連續可微分=>存在 P之neighborhood N, 使∂h/∂z≠0 由 implicit function thm: 在N內可視z為x, y之函數=> z=f(x,y) 即得曲面 z= f(x,y) (z 為 x, y之顯函數) Note:若 ∂h/∂y≠ 0...