Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 143

Mathematical terminology

This may be an obvious question, but in a mathematical context, what does "recover" mean? For example, one question on this website asked if it were possible to "recover a...

Asked on 01/23/2021 by JeremyS

0 answer

Finding saddle point from the critical points

If $(4,0)$ and $(0,-1/2)$ are critical points of the function: $$f(x,y)=5-(alpha +beta)x^2 +beta y^2+(alpha+1)y^3+x^ 3,$$where $ alpha,beta in mathbb R$ then prove that ...

Asked on 01/22/2021 by Lawrence Mano

1 answer

$1cdot3cdot5cdots(2n-1) < (frac{2n}{e})^{n+1}, n in mathbb{N}, n geq 2$ proof doesn't seem to work

I found that excercise in an old book without any hint nor solution. Olthough I know a thing ot two about induction, this one seems to be too tricky for...

Asked on 01/22/2021 by testcase12

1 answer

Ambiguity in the evaluation of a real integral multiplied by a complex number

Let's consider the following integral, where x is a real value: $int_{0}^{1}ln(i)x^{2}dx=i(frac{pi}{2}+2kpi)int_{0}^{1}x^{2}dx$. Since $ln(i)=i(frac{pi}{2}+2kpi)$, k being an integer, what value should I consider?...

Asked on 01/22/2021 by Gabriele Privitera

1 answer

Construction of a connection on a vector bundle $Eto M$ with trivial determinant bundle

I read the following statement, and I am trying to see why it is true.Let $Eto M$ be a rank 2 complex vector bundle over a smooth manifold ...

Asked on 01/22/2021

1 answer

Proving $tan^{-1}frac{1}{x} leq frac{1}{x}$

I'm not sure what I'm missing. I've done a limit comparison test that relies on $$tan^{-1}frac{1}{x} leq frac{1}{x}$$ which seems to be true for $x > 0$, but...

Asked on 01/22/2021 by Reece McMillin

3 answer

How can we show that there is a zero of $f$

Let $$f(x)= x^2+2020x+1$$ a polynomial.We define $F_n(x)$ to be $f(f(f...f(x)))$ applied $n$ times .Show that for all positive integer $nge1$ there exists a...

Asked on 01/22/2021

2 answer

Convergence in vector space

I have two questions. Let $V$ be a subspace of finite-dimensional vector space $U$. Suppose $u_kto u_0$ in $U$ as $ktoinfty$. First, for any ...

Asked on 01/22/2021

1 answer

Conditon for $f(x)$ such that $f(d(x, y))$ induces the same topology with $d(x, y)$

On Munkres' Topology, Sec 20, Q 11, for $f(x)=frac{x}{1+x}$, $f(d(x, y))$ induces the same topology with $d(x, y)$. And I have some question here : what conditions...

Asked on 01/22/2021 by random487510

1 answer

Simple $R$-module equivalent statement

I am trying to show that the two statements are logically equivalent. a) $X$ is a simple $R$-module. b) For any $x , y in X$, ...

Asked on 01/22/2021 by An Isomorphic Teen

1 answer

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