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How can be proved these statments?$lim sup (A_n cap B_n) = lim sup (A_n) cap lim sup (B_n) $$lim sup (A_n cup B_n) = lim sup (A_n) cup...
Asked on 02/04/2021
1 answerI was solving a physics problem and I wondered how could it be done using a more formal approach and without resorting to the mindset of infinitesimals When it comes...
Asked on 02/04/2021
0 answerCalculate $$lim_{nto infty} frac{1}{n^{n}}int_{0}^{n}x^narctan(sqrt[n]{x})dx$$My approach: I was trying to solve first the integral, so for example for $n=1$, we have that$$int xarctan(x)dx=frac{1}{2}x^{2}arctan(x)-frac{x}{2}+frac{1}{2}arctan(x)+c$$and for $n=2$,...
Asked on 02/04/2021
3 answerI understand that the absolute value of the determinant of a 3x3 matrix is the volume of the parallelepiped. I also understand that the determinant of a 3x3 rotation matrix...
Asked on 02/04/2021
0 answerThis may be an overly simple question, but: If I am integrating something like $$int -i dx,,$$ is this the same as $$-i int dx = -i x...
Asked on 02/04/2021
2 answerLet $v_1,...,v_k$ be vectors whose entries are all in ${ 0, 1 }$. These vectors can be considered both as elements of $Bbb{Z}_2^n = {0,1}^n$ (with modulo...
Asked on 02/04/2021 by Andrew Yuan
1 answerSay $f colon X to Y$ such that $1mapsto2, 2mapsto3, 3mapsto4, 4mapsto3, 5mapsto1, 6mapsto2, 7mapsto3$. (Here the $X ={1,2,3,4,5,6,7}, Y = {1,2,3,4,5,6}$) Find the number of the...
Asked on 02/03/2021 by se-hyuck yang
1 answerThe proof using the pumping lemma is super easy but is it possible to solve it without pumping lemma and knowing $a^nb^n$ is irregular ?...
Asked on 02/03/2021 by Parsa Noori
1 answerI am trying to help my son with a fairly basic maths question for school.How many squares are on a standard $8times8$ chess board?We have solved this one quickly,...
Asked on 02/03/2021 by user3190686
1 answerLet $Ain mathcal{L}(H)$, where $mathcal{L}(H)$ is the space of bounded linear operator, $H$ is real Hilbert space and $langle x,Ayrangle =langle Ax,y rangle,forall x,yin H$, ...
Asked on 02/03/2021
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