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I found a beautiful form of the sum of square roots. $a,b,cinmathbb{R}$begin{eqnarray*} A &:=& abc\ B &:=& a+b+c\...
Asked on 11/21/2021 by isato
1 answerFrom wiki I found the very basic definition of line integral on vector: For any partition $P={vec{x}_1,...,vec{x}_{m+1}}$ separate $L$, any pick of points $vec{xi}_iin...
Asked on 11/21/2021 by Shore
1 answerI want to prove that these two functions $f(x)$ and $g(x)$ do not intersect for $x>1$:$$f(x)=cosh left(frac{2 sqrt{2} pi x left(x^2-1right) cosh (pi ...
Asked on 11/21/2021 by user805770
1 answerIs there a way to evaluate the integral:$$int_0^1sqrt{x+sqrt{x^2+sqrt{x^3+sqrt{x^4+cdots}}}},dx,$$ without using numerical methods? The integrand doesn't seem to converge to anything for any arbitrary positive real $x$. I could...
Asked on 11/21/2021
1 answerUsing the additive properties of differentiation I proved that $V$ is a subspace. The fact that $overline{O} in V$ is also trivial. However, I am stuck as to...
Asked on 11/21/2021 by Rajesh Sri
0 answerConsidering this question where there is this integral: $$int_{0}^{4pi} ln|13sin x+3sqrt3cos x|mathrm dx tag 1$$ Easily all the periodic function $$a'sin(x)+bcos(x)+c=0 tag 2$$ can be written...
Asked on 11/21/2021
1 answerI was reading an article where in one of the steps we were trying to calculate the daily return. It saidReturn = (a / b) – 1It then said,...
Asked on 11/21/2021 by noi.m
3 answerI am trying to solve the system $$frac{dx}{dt}=0.2x^2left(1-frac{x}{3}right),$$ if $x(0)=x_0$. This is a separable ODE, and my attempt is below.begin{align}frac{dx}{dt}&=0.2x^2left(1-frac{x}{3}right) \intfrac{dx}{x^2(3-x)}&=frac{1}{15}int dt \int...
Asked on 11/21/2021
1 answer(Note: This post is an offshoot of the following earlier question.) Let $sigma(x)$ be the sum of divisors of the positive integer $x$. Denote the...
Asked on 11/21/2021 by Jose Arnaldo Bebita Dris
1 answerI have been trying to work out this problem for hours but I cannot get it. A circle has its centre on the positive $x$-axis at $(a,0)$. The...
Asked on 11/21/2021 by BillyBob3234
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