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...find tangent line at a point x0 2. find the x intercept of that tangent line 3. use the x intercept and repeat the process. newton s method ...process point (4.9,0.01) is on the curve, and the tangent line s slope through the point is 9.8 y...

.... (If we did, then we wouldn't have needed to use the axiom of choice, since the construction would have sufficed). For example: 所有向量...

[2x/ (x+1)(x-2)] +[3/(2-x)] = [2x/ (x+1)(x-2)]-[3/( x- 2)] = [2x/ (x+1)(x-2)]-[3(x+1)/( x- 2) (x+1)] = [2x-3(x+1)]/( x-2) (x+1) = (-x-3)/ ( x-2) (x+1) = -(x+3)/ ( x-2) (x+1)

use ratio test An(n為足碼)=x^n/1*3*5 …(2n-1) lim | A(n+1)/An | = | x/2n+1 | (所有lim n趨近於無限大 因為n趨近於無限大 所以lim | A(n+1)/An | = 0 for all x radius of convergence = 無限大 interval of convergence=R(實數)

...it's the same meaning here. ------------------------------------------------------------------ use a combinatorial proof of the identity ((summation)k=0 to k=n ) C(n,k)^2 = C(2n,k...

1. (a) (2x+1)(2x-1)=4x^2-1 (b) Using the result of (a), expand [2(3y+7)+1][2(3y+7)-1]. 利用(a)的結果，把(b)展開。 公式(1) a...

1. use the method of integration by part twice. let u=ln(x), du=(1/x)dx, dx=xdu, since e^u=x, so dx=e^udx so, ∫sin...2005-08-03 02:27:45 補充： oops, I forget the constant C.Put it in the very end of each answer.

δ取任意數都可以，所以就取δ = ε即可。 For all ε > 0, take δ = ε when |x - a|< δ => |c - c| = 0 < ε 得証。