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Let $a,b > 0.$ Find $int_R e^{f(x,y)}dxdy,$ where $f(x,y) = max{a^2y^2, b^2x^2}$ and $R = {(x,y) : 0leq x leq a, 0leq y leq b}.$I think...
Asked on 02/11/2021
0 answerA class consists of $23$ students. We want to create groups of $3,$in a way that all students cooperate (two students cooperate iff they coexist in...
Asked on 02/11/2021 by Nikolaos Skout
2 answerI was hoping for a hint for the following question. I though that I need to use property 3 of the definition of Atlas for to prove it (about two...
Asked on 02/11/2021 by Itamar E. Aharoni
0 answerProblem: Let $F(x)$ be a continuous and non-decreasing function on $[0,1]$ with $F(0)=0$ and $F(1)=1$. I'd like to prove the existence of a couuntably additive measure...
Asked on 02/11/2021
1 answerLet $x$,$y$ and $z$ be three linearly independent vectors. Explain, with justification, whether or not$operatorname{span}{x,,y,,z}=operatorname{span}{x+y,,y+z,,z+x}$....
Asked on 02/11/2021 by Martyna
3 answerConsider first the iterated integral $I=m!int_0^xint_0^{x_1} ... int_0^{x_{m-1}} prod_{i=1}^m dx_i f(x_i)$. By permuting the dummy indices, we can reorder $x_1$ to $x_m$ to find new expressions for...
Asked on 02/11/2021 by user196574
1 answerConsider the following example: On page 1 of my paper I write: Let $R$ be a finite commutative ring with $1$. ...[some text where I use $R$]......
Asked on 02/11/2021 by Clapham
1 answerLet $$P_n:=bigg{p:[0,1]rightarrowmathbb R :deg(p)le nbigg}$$And define the norm $$lVert p(t)rVert=max_{0le kle n}lvert a_krvert text{ where $p(t)=a_nt^n+...+a_1t+a_0$}$$We define a linear operator: $$T:P_nlongrightarrow P_n :$$...
Asked on 02/11/2021
1 answerThe question is: put one of $1,2,3,4,5,6,7,8,9$ in one position below, to obtain $100$$$largeoverline{squaresquare}+overline{squaresquare}+overline{squaresquare}=100$$his mean fintThis mean to find three,two digit number with sum of...
Asked on 02/10/2021 by Khosrotash
1 answerCan someone verify my proof this is what I have so far? Proof using the Weirstrass M. test. Assume $x in S,$ that is, $[0,1].$ Then$$|f_n(x)|=...
Asked on 02/10/2021 by NaturalMathLover
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