How many real numbers satisfy x+1=4*atan(x)?=> (x+1)/4=atan(x)=> tan[(x+1)/4]=x=> y1(x)=tan[(x+1)/4...
(1) x=7^(1/2) + 12^(1/3) satisfies (x^3-12)^2-7=0; (2) x=2 + √(-3) satisfies (x-2)^2+3=0; (3) x=cos(2π/n) + isin(2π/n) satisfies x^n-1=0; Each of the above equation is algebraic with rational coefficients.
...例子. e.g. Find real-valued differentiable functions y=y(x) satisfying the differential equation (E) (y')^2+y^2+1=0. Proof: For...
...4φφ1 4φφ2 4φφ3 | =0 so that F(x,y,z) can not satisfy the inverse fn. thm. (b) F(x,y,z)=(u,v,w)=(φ(x,y,z), φ(x,y,z), 2...
...rarr;R has a local extreme point, then the critical point M should satisfied H'(M) = 0 => f(M) = c and thus c is the image of...
... a_1, . . . , a_j−1 so that each row vector x = (x_i) of B satisfies the linear relation: j-1 x_j = Σ(a_i)(x_i) = a1x1 + ... + (a_j-1...
...a(b + c + bc) = a + b + c + ab + bc + ac + abc Associative law is satisfied . So, G is a group
...k (Σ_n μ_n)(A_k) From 1) 2) 3) => Σ_n μ_n satisfies the definition of outer measuer.
...)(a)(x-a)^k]/k！ 其中f( *k)表示f(x)微分k次 k=0 for all x satisfies x屬於I , 其中I為f(x)的收斂區間。 當a=0時，則為Maclaurin...
