Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 203

Is the union of finitely many open sets in an omega-cover contained within some member of the cover?

Let $mathcal{U}$ be an open cover of $mathbb{R}$ (Standard Topology) such that $mathbb{R} not in mathcal{U}$ and for any finite set $A$ there is a $U in mathcal{U}$ such that...

Asked on 09/23/2020 by objectivesea

2 answer

Evaluate $int_0^{pi/2} frac{arctan{left(frac{2sin{x}}{2cos{x}-1}right)}sin{left(frac{x}{2}right)}}{sqrt{cos{x}}} , mathrm{d}x$

Evaluate: $$int_0^{frac{pi}{2}} frac{arctan{left(frac{2sin{x}}{2cos{x}-1}right)}sin{left(frac{x}{2}right)}}{sqrt{cos{x}}} , mathrm{d}x$$ I believe there is a "nice" closed form solution but Wolfram is too weak. These arctan integrals are so tricky! I sense...

Asked on 09/23/2020 by user801111

1 answer

Problem with split exact sequences and free finitely generated modules

Let the sequence $$0to Ato Bto Cto 0$$ be a split exact sequence of $R$-modules over a ring $R$. The ring $R$ is a commutative ring...

Asked on 09/22/2020 by aa_bb

2 answer

Well posedness of Burgers' equation

let's consider the general Burgers' equation $$ frac{partial u}{partial t} + c(x) frac{partial u}{partial x} = nu frac{partial ^{2}u}{partial x^{2}} $$ where $c(x)$ is a periodic and bounded...

Asked on 09/21/2020 by Rage

0 answer

degree of minimal polynomial and degree of field extension

Let $K$ be a field and $a in K$ algebraic. Then we have the minimal polynomial $m_a in K[X]$ with $deg(m_a) = n = [K(a):K]$ This...

Asked on 09/20/2020 by Ton910

1 answer

The set of all finite subsets of $mathbb{R}_+$ is countable.

I'm struggling to figure out how to prove that the set of all finite subsets of $mathbb{R}_+$ is countable. I thought that it wasn't but a TA told me...

Asked on 09/19/2020 by simey

1 answer

What is the probability that balls left are white?

From a bag containing $b$ black balls and $a$ white balls, balls are successively drawn without replacement until only those of the same colour are left. What is...

Asked on 09/18/2020 by abhishek

1 answer

Dual image map restricts to open sets?

A book I'm reading on category theory says that if $A$ and $B$ are topological spaces and $f:Ato B$ is continuous, then the "dual image" map...

Asked on 09/18/2020 by blargoner

1 answer

How to compute $sum_{n=1}^infty{frac{n}{(2n+1)!}}$?

In a calculus book I am reading I have encountered the following problem: $$sum_{n=1}^infty{frac{n}{(2n+1)!}}$$ The hint is to use Taylor series expansion's for $e^x$. I tried to express...

Asked on 09/18/2020 by Samuel A. Morales

3 answer

Prove there is no rational number r such that $2^r = 3$

Prove there is no rational number r such that $2^r = 3$.I am wondering if my proof is correct. $mathbf{Proof:}$ We will provide a proof by contradiction....

Asked on 09/16/2020 by yastown

3 answer

Ask a Question

Get help from others!

Mathematics : Recent Questions and Answers (Page 203)

Ask a Question