Recent content by hedlund

CrankFan: I doesn't converge to a root if |x0| > 1. If I choose |x0| < 1 it does in fact converge to a root. So it's basicially useless for polynomials, since you need to know how big the seed needs to be for it to converge. Zurtex: I'm aware of the fact that it is slow. However I was...

Suppose f is a function. How can we solve the equation f = x? I think I've found an interesting new way, I'm not sure it's correct however. Say we want to solve the equation cos(x)=x, then a suitable way to solve this equation is to use Newton-Raphson to get a solution. But I think I've found a...

Intresting, I didn't think there were any counter-examples. It's interesting if Euler was _almost_ right and no other counter-exampel for the exponent could be found.

Fermat's last theorem states that the diophantine equation x^n + y^n = z^n does not have solutions if xyz \neq 0 and n > 2. Now and Indian mathematician, Dhananjay P. Mehendal have conjectured a generalization of FLT. His (or her, I'm no good at Indian names) states that the...

This may be the same argument as you're using, don't know really. Assume that sqrt(2) is rational, then we have p and q such as sqrt(2) = p/q. This gived 2 = p^2/q^2. But since gcd(p,q)=1 then p^2/q^2 isn't an integer unless q=1. This gives the equation 2 = p^2 with integers, no integer can...

I haven't studied Galois theory, just seen some exercises on it. However I would like to know how one can solve this problem: Show explicitly that \mathbb{Q}\left( \sqrt{2},\sqrt{3},\sqrt{5} \right) is a simple extension over \mathbb{Q} . I don't think I will understand the solution, but...

Can't you integrate sin(x)/x by using the fact that sin(x) = x - x^3/3! + x^5/5! - x^7/7! ... so sin(x)/x = 1 - x^2/3! + x^4/5! - x^6/7! ... this would give x - x^3/(3*3!) + x^5/(5*5!) - x^7/(7*7!) + C, and we know that sin(x)/x -> 1 as x -> 0, so C=1. This would give us that the antiderivate of...

Yeah your proof is easier for closure of inverses ... #2 just didn't feel right, just a feeling ... it seems rights but feels wrong. Hard to explain

Prove / disprove that \left< U_n, \cdot \right> is a group. The elements of U_n is the solutions to x^n = 1 . Example: \left< U_4, \cdot \right> is the solutions to x^4 = 1 , U_4 = \left\{ 1, -1, i, -i \right\} . And here \cdot is multiplication. So I'm wondering if this is...

Starting with: sin(x) = 2sin(x/2)cos(x/2) sin(x/2) = 2sin(x/4)cos(x/4) sin(x/4) = 2sin(x/8)cos(x/8) ... So we can arrive at this \sin{x} = 2^n \cdot \sin{\left(\frac{x}{2^n}\right)} \prod_{k=1}^{n} \cos{\left(\frac{x}{2^k}\right)} Valid for n \in \mathbb{N} \backslash \{ 0 \}...

Use this \int_{-1}^{1} \sqrt{1-x^2} - x^2 (\sqrt{1-x^2}) - (1-x^2)^\frac{3}{2} \ dx = \int_{-1}^{1} \sqrt{1-x^2} \ dx - \int_{-1}^{1} x^2\sqrt{1-x^2} \ dx - \int_{-1}^{1} \left( 1- x^2\right)^{\frac{3}{2}} \ dx And make substituion for each integral ...

\int x^n \cdot \sqrt{1-x^n} \ dx It seems as the only time this is an elementary function for n > 0 is n=1 and n=2, can you prove / disprove this? n is an integer

I need software that can calculate volumes of revolutions, the only requirement is that it runs on any of the following: * Linux (i386) * Mac OS X * Windows XP (i386) Like calculate the volume when tan x is rotated around the y-axis with upper boundaries 0.2 and lower boundraries 0.1.

Yeah it was plain stupid ... I thought of it as ln(ln(y)) :/

I've thought about this a lot ... (1) y'' + ln(y) = yx (2) ln(y'' + ln(y)) = ln(yx) = ln(y)+ln(x) (3) ln(y'' + ln(y)) = ln(y) + ln(x) (4) ln(y'' + ln(y)) - ln(y) = ln(x) (5) ln(y''/ln(y) + ln(y)/ln(y)) = ln(x) (6) ln(y''/ln(y) + 1) = ln(x) (7) y''/ln(y) + 1 = x (8) y'' + ln(y) =...