@TedShifrin I'm honestly not sure if I'm happy I figured it out or sad that it took so long but.. When given $\int_{1}^{2}\int_{x}^{x^2}dydx$ to change the order you do $\int_{1}^{2}\int_{\sqrt{y}}^{y}dxdy + \int_{2}^{4}\int_{\sqrt{y}}^{2}dxdy$
I didn't consider you had to do it in two parts, was trying to figure out how to write it all in one integral
I gotta finish a lab report but thank you for the help!
Some people shouldn’t be allowed learner’s permits, let alone driver’s licenses. I don’t usually downvote unless the OP ignores me, but this was too much of a travesty.
Consider $R=k[x,y]_{(x,y)}/(xy)$ and $S=R[\frac{x}{x+y},\frac{x}{x^2+y},\dots]$, then $(R:_{Q(R)}S)$ contains $y$, so it is non-zero. Suppose that $d \in (R:_{Q(R)}S)$. Then for all $n$, we have $d\frac{x}{x^n+y} \in R$, so $$dx \in \bigcap_{n \geq 1} (x^n+y) \subset \bigcap_{n \geq 1}(x^n,y)=(y)...
no idea what the geometric interpretation of that example is :D
I mean I understand the geometric interpretation of $R=k[x,y]_{(x,y)}/(xy)$
I like his choice of topics, he does a lot of examples for everything and covers Lie groups, vector bundles, principal bundles, the classifcation of flat bundles, characeteristic classes, complex manifolds
When solving the questions in 1st chapter Spivak, some questions can be solved using many theorems, some in the previous sections, some not. Is it really important that I stick to the axioms/theorems he has exposed, or can I use my other knowledge that i take for granted? Feels like some of the qs are supposed to be challenging but another idea eradicates this. For example, applying sine substitutions
I have a question on policies. Does context always have to mean include some partial/failed attempts? or can it be also motivation, intuition or definitions
@LukasHeger Yes, we encourage motivation, intuition coupled with why, and definitions. Most of all, we appreciate specification of what the asker doesn't understand. Including failed attempts is not necessary; but motivation, specification of why stuck is then crucial.
I have a feeling that there are some people close-voting everything that doesn't include an answer to the question "what have you tried?", but maybe that's just my feeling
lukas, it's definitely possible to provide contexts that doesn't include 'failed attempts,' depending on the problem, sometimes getting stuck makes it impossible to make an attempt. stuff about motivation/intuition, or "if X were changed to Y, i'd know how to do this because Z, but here Z doesn't apply." that kind of thing, can be good context.
lukas i have noticed that sometimes with more specialized/advanced questions, there is greater risk that people who don't know the subject matter will fail to recognize context, even if it is provided, because sometimes you need to actually know the subject matter to understand the context.
amwhy, i added in a 'sometimes' up above. people certainly accuse reviewers of doing that more often than they are actually doing that, but it does happen.
and when it happens, it tends to be not with calculus or whatever, but stuff at a level where it is more likely that most of the voters to close don't know the subject matter
in any case, i think a solution to avoiding that is providing enough english language, non jargon, non symbol discussion around the problem so that someone who doesn't know the area can still recognize that an attempt has been made to place the problem in context.
as opposed to, as you note, simply blaming the reviewer for not understanding something.
@LukasHeger Then that's fine. Reviewers here, at least a lot of us, fret more about posts simply telling us what they expect users to do for them. Including attempts is not the end-all and be-all.
lukas i certainly wouldn't put in 'throwaway' attempts, i have sometimes voted to close when it looks like someone is only complying with the letter but not the spirit of the guidelines.
@leslietownes It happens, but it is rare. And a statement in the question like "I am a graduate student studying Lie algebras," can often be enough to provide the needed context for reviewers, who can say "Oh, I don't know anything about Lie algebras. I should probably skip this one."
Also, as I have said many, many times in the past: I regard "attempts" as the absolute worst kind of context. In my ideal world, an attempt would not count for context at all (as "problem statement + attempt" is typically a good way to use Math SE as a platform for getting someone else to do your homework for you).
I would generally discourage folk from posting attempts (throwaway or not), and encourage them to focus on other forms of context, e.g. some outline of what they are studying, or why the question is interesting, or some discussion of applicable theorems or definitions.
I maybe have a bias for higher-level question in my interest areas (which is kind of natural I guess), but I think a lot of higher-level question without attempts are actually fine, not all of them of course! but the percentage of questions with absolutely zero contexts seems to be much lower than in areas such as, say calculus
@LukasHeger Sure, there exist questions where "an attempt" likely provides sufficient context for interested parties. But I believe that this set of questions is vanishingly small, and that any such question at a higher level could easily be converted to something good without "an attempt".
@XanderHenderson I responded to the sequence of peep, poop, peekaboo, cock-a-doodle-doo. They do not, collectively, lead to the conclusion: "It's about roosters". Consecutive, btw!
The 2-jet bundle $\mathcal{F}^2_M$ of a manifold $M$ is a bundle that encodes second order derivative information about smooth functions on $M$. This means that, for any point $p$ in $M$, the fiber over $p$ in $\mathcal{F}^2_M$ consists of the set of 2-jets at $p$ of smooth functions defined on a...
Hello everyone! Maybe someone can give me a hint on this calculus problem: Calculate the integral: $\int\limits_{0}^{1} \dfrac{x^{\alpha} -1}{x\cdot \ln^2{x}} - \dfrac{\alpha}{\ln{x}}dx, \ where \alpha > 0$ using the fact that $\int\limits_{0}^{1} x^{\alpha -1}dx=\dfrac{1}{\alpha}$. I tried different representations of the under-integral function, but none of them seemed to me solvable
@TedShifrin I did just now, but I was hoping there is a simpler solution xd
I'm kinda bad in determining whether integral converges continiously or not: here we should consider $\int\limits_{0}^{1} x^{\alpha -1}dx$. I know it looks simple, but I'm a bit lost here answering the question whether it converges continiously on $(0, +\infty)$
Oh, sorry, yeah, I'm fuzzy. $I'(\alpha)=\dfrac{1}{\alpha}$, because if we differentiate by parameter $\alpha$ our function $\dfrac{x^{\alpha-1}-1}{\ln{x}}$ we get $x^{\alpha-1}$
Are you differentiating the original integral or the one you got integrating by parts?
Oh, I see, you're evaluating the integral we got integrating by parts by differentiating. I did the original. OK, cool. So what about the "constant" term in your integration by parts? What happened to it?
I have flagged this question. A different user (with no rep) posted it a week ago, identically with the same picture and words. I gave a solution with discussion of envelopes. I can no longer find that post. I now suspect it's a competition question somewhere.
for the space of normal distribution with mean 0 and variance sigma does it make sense to take the variance parameter to be discrete, like in the naturals? considering space of normal distributions with mean and variance as parameters, can identify the manifold to be the upper half plane given that the mean runs over the reals and the variance is positive
Shoot, you can’t draft people to be interested in your particular question. You’re better off posting a well-written question on the main site, where it will get a much wider audience.
