that seems like a really good option. i only recently (last month or so) bit the bullet and purchased a mathematica license. i still am getting used to it but the way it handles functions is nicer than anything else ive worked with.
I'm sorry to bother this chat with simple and trivial questions but why is it that the polynomials of degree $\leq 2$ form a set of representatives for $\mathbb{Z}_3[X]/(X^3+1)$?
WTH does this even mean "If we start at c and nudge x a little to the right, f(x) changes by f’(c) times the amount we changed x. If this factor is positive, then f(x) changed by a positive amount, so ff is increasing near c."?
Maybe this is a silly question but for two real functions $f$ and $g$, does $f\leq g$ always just mean a pointwise comparison of $f(x)$ and $g(x)$ for all $x$ in the domain?
I have seen it used for that. But yes a bit ambiguous
If I defined a geodesic between two densities via the wasserstein metric will the result also be a density ? ( i.e will it be absolutely continuous to the lebesgue measure
@TedShifrin can you give out yesterday's question?
Find the value of $\lambda$ so that the points p q r s on the sides OA, OB ,OC and QB respectively of a regular tetrahedron OABC are coplanar. It is given that $\frac{OP}{OA}=\frac{1}{3}, \frac{OQ}{OB}=\frac{1}{2},\frac{OR}{OC}=\frac{1}{3} $ and $\frac{OS}{AB}=\lambda$
@SrijanM.T if A is not 2 or 3, then as x approaches 2(or 3), the function will approach $\infty$. So A must be 2 (or 3), in which case the limit as x approaches 2(or 3) becomes -1 (or 1). I.e finite.
@Rover Here's the general result you should try to prove (using determinants or cross products). If $A,B,C$ are the vertices of a triangle and $X$ is a point in the plane, you can write $X=\lambda A + \mu B + \nu C$ for unique scalars $\lambda,\mu,\nu$ with $\lambda + \mu + \nu = 1$. And the geometric interpretation is that, for example, $\nu$ is the ratio of the (signed) area of $\triangle $ABX$ to the area of $\triangle ABC$.
@TedShifrin does anything obvious stand out to you as a solution for this PDE? $\partial_t \rho = -v \cdot \nabla_x \rho + \nabla_v \cdot ((\gamma v + \nabla U(x)) \rho - \frac{k_B T}{\gamma} \nabla_v \rho)$
if we had $-v \cdot \nabla_x \rho = 0$, then the solution is $C e^{-U(x) / k_B T}$
is it possible to show the collatz squence starting in $s$ must hit the same value twice?
oh nvm
If the conjecture is false, it can only be because there is some starting number which gives rise to a sequence that does not contain 1. Such a sequence would either enter a repeating cycle that excludes 1, or increase without bound. No such sequence has been found.
could i ask a favor, could someone glance at math.stackexchange.com/questions/4131027/spivak-calculus-7-ch-22-convergence-of-a-continued-fraction-sequence/4134805#4134805 and tell me if i am missing something obvious please? i'm trying to understand why it is marked for deletion.
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@copper It doesn't look deleted to me. I guess the problem is the people who keep posting absolutely zero effort questions. I'm no longer answering those.
i guess that is where is feel strain with mse; some habits acquired over a lifetime are not easily changed, partly age but also because they are normal human interaction skills.
Yeah. Sometimes the more zealous of those who speak out against question posters not putting effort into their questions, would rather comment, downvote, and flag, rather than improving the question. In this case, simply copying the comment into the question would have sufficed. Perhaps they are worried about giving their effort to the reputation of the OP.
who cares about the reputation? improve the site. improve the questions, when it is easy to do so.
@TedShifrin, je n'avais pas de réponse ; alors je suis parti du chat. Je viens d'arriver sur le site depuis quelques semaines seulement et je suis un peu perdu.
If the range of this function $f(x)$=$\frac{x-A}{x^2-5x+6}$ = R. Then, solve for A .
How can I solve this question.
