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Apr
14
accepted ODE arising in physics
Apr
14
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14
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14
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Apr
14
comment ODE arising in physics
@CameronWilliams WA's answer should be correct, but it is not enlightening at all. I would appreciate learning about the process of how to solve it :)
Apr
14
asked ODE arising in physics
Apr
11
comment limit of sequence of quotients of sequence that converges
@user3697301 Intuitively, it is correct because it would grow faster than an unbounded geometrical summation. Can you continue?
Apr
11
answered Volume of a region?
Apr
9
comment $\lim_{(x,y)\to (0,0)}\frac{\sin^3x}{x^2+y^2}$
$y$ wasn't ever necessary, not even polar coordinates :) $$ 0 \leq \left|\frac{\sin^3{x}}{x^2+y^2}\right| \leq \frac{|x|^3}{x^2+y^2} \leq \frac{|x|^3}{x^2} $$
Apr
1
comment How to evaluate $\left(\cos{\frac{5\pi}{9}}\right)^{11}+\left(\cos{\frac{7\pi}{9}}\right)^{11}+\left(\cos{\frac{11\pi}{9}}\right)^{11}$
@JyrkiLahtonen That's true...
Apr
1
comment How to evaluate $\left(\cos{\frac{5\pi}{9}}\right)^{11}+\left(\cos{\frac{7\pi}{9}}\right)^{11}+\left(\cos{\frac{11\pi}{9}}\right)^{11}$
Say your each term(without the exponent) is $x,y,z$. Then $x,y,z$ are the three solutions of $\cos\alpha$ in $$1/2=\cos3\alpha=4\cos^3\alpha-3\cos\alpha$$
Mar
28
comment is it possible to find $x$ where $y$ is equal to a whole number in a non iterative fashion
Any solution to this problem(with arbitrary coefficients) would solve an arbitrary factoring with the same complexity. You can trivially test all divisors in $O(\sqrt{d})$ time. How huge are those numbers going to be?
Mar
25
comment Find the smallest postive integer $n$ such $H(n)<H(n+1)$
Now that you have edited it, columbus8's comment finishes it. $n=9$ doesn't need that many trial verifications.
Mar
25
comment Find the smallest postive integer $n$ such $H(n)<H(n+1)$
What is $f$? $f=H$ ?
Mar
25
comment is it possible to find $x$ where $y$ is equal to a whole number in a non iterative fashion
An algorithm would just find the divisors $d_i$ of $404169$ and then set $x_i=d_i-637$. That would find all solutions.
Mar
25
comment is it possible to find $x$ where $y$ is equal to a whole number in a non iterative fashion
$$y=635-404169/(637+x)$$ 637+x must be a divisor of $404169$, so...
Mar
24
comment Is $\sum_{n = 1}^{\infty} v_p(n) 2^{-n+1}$ a rational number?
@A.P. Consider the sum until $n=2^k$, you will find no period. Now until $2^{k+1}$, and induct.I have not worked out the details, but it should work. For your second question, I cannot really answer it because I lack the knowledge ;)
Mar
18
comment I am getting $i^{-1}=\pm i$.
Multipñy and divide by $i$. The square root is only defined for nonnegative reals.