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I recently learned that two independent random variables $X$ and $Y$ must have a covariance of $0$. That means that the correlation between them is also ...
Asked on 11/24/2021
3 answer$$intfrac{1}{sqrt {2x} - sqrt {x+4}} , mathrm{dx}$$ I have tried $u$-substitution and multiplying by the conjugate and then apply $u$-substitution. For the $u$-substitution, I...
Asked on 11/24/2021 by Flinn Bella
3 answerHow can I integrate $$int dfrac{dx}{(x^2-4x+13)^2}?$$Here is my attempt: $$int dfrac{dx}{(x^2-4x+13)^2}=int dfrac{dx}{((x-2)^2+9)^2}$$ Substitute $x-2=3tantheta$, $ dx=3sec^2theta dtheta$ begin{align*}&=int dfrac{3sec^2theta dtheta}{(9tan^2theta+9)^2}\&=int dfrac{3sec^2theta dtheta}{81sec^4theta}\&=dfrac{1}{27}int...
Asked on 11/24/2021 by user809843
9 answerLet $X$ be a real closed field. Let us call a subset of $X$ definable if it is definable using a first-order formula in the language of...
Asked on 11/24/2021
2 answerHow can I prove that the following are happening ($xtoinfty$): $lnBig(1+frac{1}{x}Big)=frac{1}{x}+oBig(frac{1}{x}Big)$ and $Big(1+frac{1}{x}Big)^{p}=1+frac{p}{x}+oBig(frac{1}{x}Big)$, where o is the notation for Little-o.I thought it could be shown directly...
Asked on 11/24/2021 by AndVld
2 answerHaving a dataset/timeseries consisting of $x,y$ and time for n people I need to determine whether one person was close to another for more than m minutes. Consider that...
Asked on 11/24/2021
1 answerI am trying to understand correctly the idea of uniform convergence in power series, and in general the notation for series of functions. When we define a series of functions,...
Asked on 11/24/2021
1 answerI was trying to prove L'Hospital's rule when $L= displaystyle limlimits_{x to a}dfrac {f(x)}{g(x)}$=$dfrac {infty}{infty}$. So this is what I currently tried to prove that...
Asked on 11/24/2021 by BlackThunder
1 answerI am struggling with this. If $p=frac{(x+y)}{2}$ and $q=frac{y}{x}$ and you know the values for $p$ and $q$, can you calculate what $x$ and ...
Asked on 11/24/2021
1 answerLet $R,M$ be commutative rings and $I$ be any ideal of the ring $R$.What is (are) sufficient (and necessary) condition(s) on $R$, so that given any...
Asked on 11/24/2021 by Cloud JR K
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