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I am looking for primes that would satisfy this equation: $p_1 + p_2 +p_3+p_4 = p_1 p_2 p_3 p_4 - 15$ I started by proving that an odd amount...
Asked on 12/12/2020 by vlnkaowo
4 answerThis is probably a trivial question in arithmetic. Given a number $x=0.a_{1}a_{2}...$ which never terminate. If we do a multiplication with an integer $N$, in real life of...
Asked on 12/12/2020 by Ken.Wong
2 answerIntroductionWe want to define a measure for determining whether one subset of $mathbb{R}$ is bigger than the other. I am have defined such a measure, but I am not...
Asked on 12/11/2020 by Samuel Muldoon
1 answerI'm thinking the condition is that the original graph G must have half of edges than its complete graph, but I'm not sure if that's correct. I appreciate any help,...
Asked on 12/11/2020 by Isaac_42
0 answerScenario A: Assume you can invest $40,000 each year starting at age 23 and ending at age $n$, earning a 7% return. Assume you leave the money invested until...
Asked on 12/11/2020 by jippyjoe4
1 answerA lecture slide from numerical analysis shows how the taylor series is taken. $$frac{u_{i+1}-u_{i}}{h}=u_{i}^{prime}+frac{h}{2} u_{i}^{prime prime}+frac{h^{2}}{6} u_{i}^{prime prime prime}+mathcal{O}left(h^{3}right)$$ I normally do not have trouble with the Taylor series,...
Asked on 12/10/2020
0 answerShow that $Vert vVert^2= langle v,AA' vrangle iff AA'=I$. My thoughts: let $AA'=M$. Then, the above implies$$sum^n_{i=1}(1-M_{ii})v_i^2+sum^n_{i=1}sum^n_{jneq i}v_iM_{ij}v_j=0.$$How would one go about showing...
Asked on 12/10/2020 by chuck
1 answerHere is a new challenging problem: Show that $$I=int_0^{pi/2} xfrac{ln(cos x)}{sin x}dx=2ln(2)G-frac{pi}{8}ln^2(2)-frac{5pi^3}{32}+4Imleft{text{Li}_3left(frac{1+i}{2}right)right}$$ My attempt: With Weierstrass substitution we have $$I=2int_0^1frac{arctan x}{x}lnleft(frac{1-x^2}{1+x^2}right)dxoverset{xto frac{1-x}{1+x}}{=}4int_0^1frac{frac{pi}{4}-arctan x}{1-x^2}lnleft(frac{2x}{1+x^2}right)dx$$ $$=piunderbrace{int_0^1frac{1}{1-x^2}lnleft(frac{2x}{1+x^2}right)dx}_{I_1}-4underbrace{int_0^1frac{arctan x}{1-x^2}lnleft(frac{2x}{1+x^2}right)dx}_{I_2}$$...
Asked on 12/10/2020
3 answerI would like to evaluate the following limit: $$limlimits_{xto3} (4 - x)^{tan (frac {pi x} {2})} .$$My working begin{align}limlimits_{xto3} (4 - x)^{tan (frac {pi x} {2})}...
Asked on 12/10/2020 by Ethan Mark
3 answerThe book seems to cover interesting topics and I read an old review which said the book would be helpful in showing students the concrete side of analysis before delving...
Asked on 12/10/2020 by Mert Baştuğ
1 answerGet help from others!
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