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I have two functions $f(x)$ and $g(x)$ for $x>0$. Both functions are monotonically increasing and $f(x)>5$ and $g(x)>0$ . I know that $f(x)>sqrt{g(x)}$. Then,...
Asked on 12/13/2021 by user807688
1 answerI'm trying to solve the integral $$intintfrac{dxdy}{sqrt{x^2+(y-y_0)^2+R^2}}$$but not getting very far. It should have limits and in polar coordinates it is up to some fixed angle theta. R...
Asked on 12/13/2021
1 answerFor $K$ a number field, ${alpha_1, dots, alpha_n}$ a basis of $K/mathbb{Q}$ and $M = mathbb{Z}alpha_1 + dots + mathbb{Z}alpha_n$, the corresponding ring of multipliers is...
Asked on 12/13/2021 by kaedit
1 answerLet $varphi$ be differentiable. Show that $$phi: mathbb R^n to mathbb R^n, x mapsto varphi(lVert xrVert_2) x$$ is (total) differentiable where $x neq 0$. How can I...
Asked on 12/13/2021
1 answerI'm working through a statistical physics book and one of the problems makes the claim that the quantity: $$H =frac{1}{N}sum_{n=1}^Nfrac{1}{frac{a}{N} + frac{b}{N^{5/3}}(n^{5/3}-(n-1)^{5/3})}$$can be expressed in the large ...
Asked on 12/13/2021 by hallowdance
1 answerAre there any textbooks in linear algebra, analysis, or algebra which provide a summary of the ideas presented in the chapter? A similar question has been asked earlier List...
Asked on 12/13/2021 by SARTHAK GUPTA
4 answerLet $P$ be a positive scalar function and $mathbf{v}(mathbf{x})$ is an assigned smooth vector field. The quantity $P(t,mathbf{x})$ evolves according to a transport equation...
Asked on 12/13/2021
0 answerI have two orthogonal vectors $a$, $b$, which lie on a unit sphere (i.e. unit vectors). I want to apply one or more rotations to the sphere such that $a$...
Asked on 12/13/2021 by stephent
2 answerI have the following function: $100/(50 + sqrt{(a + sb)/sc}) $ where a, b, and c, are constants and $s=jomega$. I have tried using inverse Laplace calculators online,...
Asked on 12/13/2021
0 answerI need to simplify the following expression in a way that introduces minimal floating point cancellation errors. $$(1+x^2 )^{frac{1}{2}}-(1-x^2 )^{frac{1}{2}}$$ The errors accumulate when numbers close together are subtracted...
Asked on 12/13/2021
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