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# Mathematics : Recent Questions and Answers

Find answers to your questions about Mathematics or help others by answering their Mathematics questions.

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 ## The topology generated by open intervals of rational numbers Let$B = { mathbb{R} } cup { (a,b) capmathbb {Q} , alt b , a,b inmathbb{Q}}$Thus, a set$V in B\$...

Asked on 01/07/2022 by roslavets