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$fleft(x,yright)=e^{x+y}left(x^{frac{1}{3}}left(y-1right)^{frac{1}{3}}+y^{frac{1}{3}}left(x-1right)^{frac{2}{3}}right)$What's the value of $frac{partial }{partial x}left(fleft(x,yright)right)$ at $(0,1)$? There two solutions below. Why are the answers different? Answer 1:$fleft(x,1right)=e^{x+1}left(x-1right)^{frac{2}{3}}$$frac{partial }{partial :x}left(fleft(x,1right)right)=e^{x+1}left(x-1right)^{frac{2}{3}}+frac{2}{3}e^{x+1}left(x-1right)^{-frac{1}{3}}$so $frac{partial}{partial x}left(fleft(0,1right)right)=frac{e}{3}$Answer...
Asked on 11/06/2021 by ikigai
2 answerAll texts I have seen about Martin's Axiom briefly mention that it is independent of ZFC, that it is implied by CH and that it is relatively consistent with ZFC+(not...
Asked on 11/06/2021 by Grinsekotze
1 answerSuppose you have an ellipsoid given by the set, $$left{ x inmathbb{R}^3 mid x^TQx = 1 right}$$ where $Q = mbox{diag}(a,b,c)$. Is there a way to parametrize the...
Asked on 11/06/2021
0 answerHow do I find supremum of set ? $ (0,1) capBbb{Q}$ , where $Bbb Q$ is set of al rationals. How will answer change if rationals...
Asked on 11/06/2021 by Jessica Griffin
4 answerWe have the following equation p=(1+s)p(A+dl) where p is an unknown vector, d as well as l are given vectors, s a constant and A a diagonal matrix. Would it...
Asked on 11/06/2021 by LoneWolf
0 answerI have a series: $$sum_{n=1}^{infty} frac{1}{4^{2n-1}}$$ I know that $sum_{n=1}^{infty} frac{1}{4^{n}} = frac{1}{1-frac{1}{4}}=frac{4}{3}$, but what should I use in my case?...
Asked on 11/06/2021 by manabou11
1 answerThe typical way of summing $S_g(n,x) = 1+x+x^2+cdots+x^n$ by multiplying by $(1-x)$ is well known. The arithmetico-geometric series $S_{ag}(n,x) = 1+2x+3x^2+4x^3+cdots+(n+1)x^n$ can be summed in one of...
Asked on 11/06/2021
2 answerFrom Rotman's Algebraic Topology:If $K$ is a connected simplicial complex with basepoin $p$, then $pi(K,p) simeq G_{K,T}$, where $T$ is a maximal tree in $K$...
Asked on 11/06/2021
1 answerI'm wondering about how to show compute this series: $$sum_{n=0}^{infty}(-1)^{n-1}binom{1/2}{n}$$ My approach was to use the general formula of the binomial series, which is: $$(1+z)^r=sum_{k=0}^{+infty}z^{k}binom{r}{k}$$ Yet this can't...
Asked on 11/06/2021 by PortoKranto
1 answerSo I found this problem where you're given a differential equation: $$frac{dy}{dx}= sqrt{frac{c}{x}}$$ And solved it to get $$y = -frac{2}{3sqrt{c}}.x^{frac{3}{2}} + A$$ Where A is an arbitrary...
Asked on 11/06/2021 by Rahul Silva
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