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I was asked to find the smallest $sigma$-algebra ($sigma(Z)$) generated by the following set $Z$={{1,2},{2,3},{3,4}} where the sample space is $Omega$={1,2,3,4}. The thing is that the...
Asked on 12/17/2020 by Puigi
2 answerConsider the cauchy problem, $5u_x+2u_y=7$ with $u=1$ in line $2x-5y=0$. Does it has no solution, unique solution or infinitely many solution? Characteristic is parallel to the initial...
Asked on 12/17/2020
1 answerUse the appropriate eigenfunction expansion (if it exists) to represent the best solution of the following problems. $$u''+ u =f(x)$$ with boundary condition $$u(0) = u(2pi), u'(0) =...
Asked on 12/17/2020 by Rubidium.
0 answerWe are given the following $ntimes n$ matrix, whose terms are:$a+b$ for the terms in the diagonal ($i=j$).$a$ for the rest of the elements.I know we...
Asked on 12/17/2020 by Uri Toti
4 answerThe Euler-Mascheroni constant is defined as $gamma := lim_{xtoinfty}(H_n - ln,n)$ where $H_n = sum_{k=1}^{n}frac{1}{k}$, and the de la Vallée-Poussin's formula states that:$$gamma = lim_{ntoinfty}frac{1}{n}sum_{k=1}^{n}left(leftlceil frac{n}{k}...
Asked on 12/16/2020 by user834302
1 answerGiven 10 people $P_1, P_2, ldots,P_{10}$ how many 6-member teams can be formed if at most one of $P_2, P_4$ can be chosen?Either one of P2...
Asked on 12/16/2020 by Scott
1 answerLet $ABCD$ be a cyclic quadrilateral and let $AB$ and $CD$ meet at $E$. Let $M= (EBC)cap (EAD)$. Prove that $OMperp EM$ I took...
Asked on 12/16/2020 by Raheel
1 answerI am trying to figure out how to compute the limit $$lim_{t rightarrow infty} int_{-1}^1 frac{cos^2(t^3x^{10})}{tx^2 + 1} , dx.$$ If I exchange the limit and integral (when is...
Asked on 12/16/2020 by E2R0NS
2 answer$AIKJ$ is a square and $mathrm{area}(AIKJ) = mathrm{area}(Delta BCA)$. How can I prove $triangle BMI +triangle NCJ = triangle MKN $ in area. I know its true...
Asked on 12/16/2020 by Kevin Duran
0 answerI am given the partial differential equation $rho u_{tt}(x, t) + Ek^2u_{xxxx}(x, t) = 0$ for modelling a beam/rod, where $0 < x < l$, where $l$...
Asked on 12/16/2020 by The Pointer
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