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Let p(x) be the least degree polynomial equation having $sqrt[3]{7}$ + $sqrt[3]{49}$ as one of it's roots, Then product of all roots of p(x) is ?Following from...
Asked on 01/05/2022
1 answerLet $X_1,cdots,X_n stackrel{i.i.d}{sim} mathcal{N}(theta,tautheta)$, where both parameters $tau,theta$ are positive. $(a)$ Derive the likelihood ratio test of $H_0 : tau = 1$, $theta$ unknown,...
Asked on 01/05/2022 by Confuse_d
1 answerIf $a>b$ and $b<c$, and $a$ and $c$ are positive, under what conditions is $a<c$? I am just curious to know. I know that the...
Asked on 01/05/2022
3 answerBackgroundI am teaching senior high school students about the structure of numbers.Start from defining $mathbb{Q}$ and $mathbb{R}$ as the rational and real numbers respectively, we can define...
Asked on 01/05/2022 by Unreal Engine 5 Coming Soon
2 answerShow that $|uv^T-wz^T|_F^2le |u-w|_2^2+|v-z|_2^2$, assuming $u,v,w,z$ are all unit vectors....
Asked on 01/05/2022
3 answerLet $f,g$ be holomorphic function in $mathbb{D}$ that are continuous in $overline{mathbb{D}}$. Show that if $f=g$ on $|z|=1$, then $f=g$ It seems like identity...
Asked on 01/05/2022
1 answerLet$$f(x):=left{ begin{array}{ll} e^{-frac{1}{1-|x|^2}}, & hbox{$|x|<1$;} \ 0, & hbox{$|x|geq1$.} end{array}right.$$ This is a generic...
Asked on 01/05/2022 by Medo
0 answerwhat is the value of this integral ?$$int_0^infty frac{cos(log(x))}{1+x^pi}sin(x),dx=text{?}$$we have $$cos(log(x))=sum_{n=0}^infty frac{(-1)^nlog(x)^{2n}}{2n!}$$ And from it we find $$int_0^infty frac{cos(log(x))}{1+x^{pi}} = sum_{n=0}^infty frac{(-1)^{n}}{(2n)!}int_0^infty frac{log(x)^{2n}}{1+x^pi}sin(x) , dx$$ ...
Asked on 01/05/2022 by Bachamohamed
0 answerIs there a reason for the Laplace Transform starting at zero? Could the transform go from -1 to ∞ or 1 to ∞? I understand that the upper bound is...
Asked on 01/05/2022 by jonathan x
1 answerI am trying to find the relative extrema of$$f(x, y) = sin(x) + sin(y) + sin(x+y), text{ where } (x, y) in (0, 2 pi) times...
Asked on 01/05/2022
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