Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 46

Evaluate $ cos a cos 2 a cos 3 a cdots cos 999 a $ where $a=frac{2 pi}{1999}$

Evaluate$cos a cos 2 a cos 3 a cdots cos 999 a$where $a=frac{2 pi}{1999}$I know this question has already been answered many times but...

Asked on 12/08/2021

1 answer

Uniformly continuous and differentiable

I have this question. I know that a differentiable function is continuous and that a differentiable function with bounded first derivative is lipschits continuous. Now i wanted to know if...

Asked on 12/08/2021

0 answer

Is there a thing as a "Negative Dimensional Space"?

I am wondering if there is a pure mathematical, abstract, extension of the Euclidean space for negative dimensions. Do you know any studies in topology, regarding this matter?I did a...

Asked on 12/08/2021

0 answer

Are the rationals minus a point homeomorphic to the rationals?

A while ago I was dreaming up point-set topology exam questions, and this one came to mind: Is $mathbb Qsetminus {0}$ homeomorphic to $mathbb Q$? (Where both sets have the...

Asked on 12/08/2021 by Cheerful Parsnip

3 answer

Edited: Let $I=int_{0}^{pi/2}(sin 2x)^{1/3}sin x dx$ $J=int_{0}^{pi/2}(cos 2x)^{1/3}cos x dx$. Find $I/J$

Edit:Sorry guys I made an error in question, I have edited it now.I found $$I=int_{0}^{pi/2}(sin 2x)^{1/3}sin x dx = 2^{1/2}int_{0}^{pi/4}(cos 2x)^{1/3}cos x dx$$$$J=int_{0}^{pi/2}(cos 2x)^{1/3}cos xdx=2^{1/2}int_{0}^{pi/4}(sin...

Asked on 12/08/2021 by Aspirant

3 answer

Abelian finite groups and their subgroups

I have asked a similar question about 40 days ago, it did not generate any answers perhaps because it was not well formulated. So I have deleted it. Here is...

Asked on 12/08/2021 by markvs

2 answer

Painting the edges of an $n$-gonal prism with 3 colors all the edges of each vertex have different colors if $n= 2018$ and $n= 2019$?

Is it possible to paint the edges of a n-gonal prism with 3 colors so that each face has all 3 colors and all the edges of each vertex have...

Asked on 12/08/2021

2 answer

A question for a measurable function $g$ on a finite measure space such that $fgin L^p$ for all $fin L^p$

Let $mu$ be a finite positive measure on $X$ and let $1leq p<infty$. Suppose that $g:Xto Bbb R$ satisfies $fgin L^p$ whenever $fin L^p(mu)$....

Asked on 12/08/2021 by blancket

1 answer

Integral of a logarithmic derivative of a complex polynomial over the real line

Let $f(z)$ be a complex polynomial with $n$ zeros in $y>0$, $m$ zeros in $y<0$, and no real zeros. How can we show that...

Asked on 12/08/2021 by user302934

1 answer

Relation between spectral radius when the norms are equivalent

If two operator norms are equivalent on B(X), set of all bounded operators on a Banach space X, whether the corresponding spectral radii are the same? If so, please provide...

Asked on 12/08/2021 by Math Lover

1 answer

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