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How can I transform graph image into a tikzpicture LaTeX code?

I'm trying to draw in latex but I can't. Don't spare your help for drawing in complex analysis. For example, how do we draw the following multiply connected domain in...

Asked on 12/12/2023 by Jonibek

0 answer

Why should this result be true? If $f: [0,1] to mathbb{R}$ is differentiable, $g$ is continuous, and $f'(t) = g(f(t)),$ then $f$ is monotonic.

If $f: [0,1] to mathbb{R}$ is differentiable, $g$ is continuous, and$f'(t) = g(f(t)),$ then $f$ is monotonic.Example 1: Suppose $g(x) = x Rightarrow f'...

Asked on 01/07/2022

1 answer

Evaluate $int_0^1frac{mathrm{e}^{12x}-mathrm{e}^{-12x}}{mathrm{e}^{12x}+mathrm{e}^{-12x}},mathrm{d}x$

My work so far $${displaystyleint_0^1}dfrac{mathrm{e}^{12x}-mathrm{e}^{-12x}}{mathrm{e}^{12x}+mathrm{e}^{-12x}},mathrm{d}x$$ using substitution with $u=mathrm{e}^{12x}+mathrm{e}^{-12x}$ $$={displaystyleint}dfrac{1}{12u},mathrm{d}u$$ $$=class{steps-node}{cssId{steps-node-1}{dfrac{1}{12}}}{displaystyleint}dfrac{1}{u},mathrm{d}u$$ $${displaystyleint}dfrac{1}{u},mathrm{d}u$$ which is the standard integral: $$=lnleft(uright)$$ $$=dfrac{lnleft(uright)}{12}$$ and using substitution with...

Asked on 01/07/2022

4 answer

Find an example of sets of cosets of different cardinality

$G$ is a finite group. Let $H$ be a subgroup of $G$. Is there an example of $G$ and $H$ such that$${rm Card}({Hxhmid...

Asked on 01/07/2022

3 answer

Prime number checker formula

First let $N = p^2$. I think that to show that any number less than $N$ is prime, you only have to check to show it has factors...

Asked on 01/07/2022 by Mondo Duke

2 answer

About holomorph of a finite group being the normalizer of regular image

Here is part of Exercise 5.5.19 in Dummit & Foote's Abstract Algebra:Let $H$ be a group of order $n$, let $K=operatorname{Aut}(H)$ and $G=operatorname{Hol}(H)=Hrtimes K$ (where ...

Asked on 01/07/2022

1 answer

How do you generally tell the independence of events in a probability problem when it is not outright stated?

First question, do probability problems generally consisting of two categories always assume two events are dependent? Let's say there are two categories from a set of n people. They are...

Asked on 01/07/2022

0 answer

Why this map is birational?

Let $Y$ be a connected normal Noetherian scheme, $f: Xto Y$ is an etale morphism of finite type. We assume $X$ is also connected. I have proved...

Asked on 01/07/2022

0 answer

Relationship between multivariate Bernoulli random vector and categorical random variable

For simplicity, I'll focus on the bivariate case. Let $(X_1,X_2)$ be a random vector that obeys bivariate Bernoulli. $X_i$ takes either zero or one. The associated pdf can...

Asked on 01/07/2022

1 answer

Can't argue with success? Looking for "bad math" that "gets away with it"

I'm looking for cases of invalid math operations producing (in spite of it all) correct results (aka "every math teacher's nightmare"). One example would be "cancelling" the 6's in ...

Asked on 01/07/2022

41 answer

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