limit at infinity quotient by x privided given function uniformly continuous
Asymptotics of uniformly continuous functions over $\mathbb R$
Can I delete files or folders from /private/var/folders/? I have this folder /private/var/folders/bf/ with 3GB of what seems temporary files. Can I delete this folder? What is the justification for locking votes? Why am I not allowed to change my vote after some period of time? There are times when I go back to things I voted on, and decide they didn't deserve that specific vote. (I get wiser as I grow older) What can you say about $f$ and $g$ in the case that $fg$ is 1) Injective, 2) Surjective - Cohn - Classic Algebra Page 15 How do you send a HEAD HTTP request in Python 2? What I'm trying to do here is get the headers of a given URL so I can determine the MIME type. I want to be able to see if http://somedomain/foo/ will return an HTML document or a JPEG image for example. Thus, I need to figure out how to send a HEAD request so that I can read the MIME type without having to download the content. Does anyone know of an easy way of doing this? I need to find all group homomorphisms of $S_n\to\mathbb{C}^*$ (for $n\ge2$), and also all group homomorphisms of $A_n\to\mathbb{C}^*$ (for $n\ge2$).  Someone on this site, two years ago, seems to have already asked the same question (). I understand what the questioner says there, but I don't understand it when he says:     Therefore there is exactly one $g:\mathbb{Z}/2\mathbb{Z}\to\mathbb{C}^*$, so all elements of $a\in\mathbb{C}^*$ give us $\operatorname{ord}(a)\mid g[\mathbb{Z}/2\mathbb{Z}]$, so $a$ can only be $-1$ or $1$. Now we know that $f:S_n\to\{-1,1\}$ &hellip;   What is he saying there? And how to go on from there? (I do not understand the answer given either &hellip;)  I hope that someone here can help me further. (And if I'm not allowed to ask this question because is has already been asked two years ago, please tell me what to do instead).  Thank you in advance! Variation of Pythagorean triplets: $x^2+y^2 = z^3$ Suppose that $f:\Bbb R\to \Bbb R$ is continuous and that $f(x)\to 0$ as $x\to \pm\infty.$Prove that $f$ is uniformly continuous. Suppose that $f:\Bbb R\to \Bbb R$ is continuous and that $f(x)\to 0$ as $x\to \pm\infty$. Prove that $f$ is uniformly continuous.   Since $f(x)\to 0$ as $x\to \pm\infty$ we have $|f(x)|&lt;\epsilon $ whenever $x&lt;-K$ and $x&gt;K$ where $K&gt;0$.  Also $f$ is uniformly continuous on $[-K,K]$ as the domain is compact.  Hence $f$ is uniformly continuous in $(-\infty,-K)\cup [-K,K]\cup (K,\infty)$.  But how to conclude that $f$ is uniformly continuous on $\Bbb R$ from above as I may chose $x\in (-\infty,-K);y\in [-K,K]$ ,how to conclude that $|f(x)-f(y)|&lt;\epsilon $ from above for a given $\epsilon$?  Please suggest the edits required. What does "preceding" mean in Oracle? I have Ubuntu on my laptop. Now I want install Windows 7 in a dual-boot. How can I do this? I can't lose my Ubuntu files, and I'm afraid that I might break . Go  for UEFI only! Why bother with the dual problem when fitting SVM? How can I run a Minecraft Server on multiple CPU cores? I am working on setting up a Minecraft server on a machine I have at home. This particular machine has two quad-core CPUs running at 2.0Ghz so I would like to take advantage of the number of cores and run a server with 4 or 6 of the cores. My server of choice is CraftBukkit, the latest version of which is craftbukkit-1.4.7-R1.0 and launched with a start-up script of:  "C:\Program Files\Java\jre7\bin\java.exe" -Xms1G -Xmx8G -jar craftbukkit-1.4.7-R1.0.jar"   The  says:     Minecraft servers, as of 1.1.0, can use multiple cores, so now they will not sit idle.   but does not really expand on this.  My questions, then:   Is it possible to set the number of cores the server uses? How do I do it - via start-up options, or other methods? Is it really worth it and would it make that much of a difference with a lot of players? I am trying to solve the exercises from the book Stochastic differential equations -An Introduction with applications by Bernt Oksendal and I am stuck on 1 question.  Prove directly from the definition of Ito's integral that   $$\int_0^t B_s^2 dB_s=\frac{1}{3}B_t^3-\int_0^t B_s ds$$  I have tried for a couple of hours but I simply cannot prove it . I would be grateful if somebody could help me out , even a hint would be very helpful What are the different colors on the unity launcher icons? Example:      My question is simple.  What are the different colors representing in the unity launcher background for each icon.  I mean, it seems consistent (firefox is always orange), but it's not jumping out at me what the pattern is.  On my screen, it's:   Firefox: Orange Chrome: Yellow Terminal: Grey RDP App: Blue KeyPassX: Green NetBeans: Blue   I'd like to turn it off if possible, but first I'd like to understand more about it.  Any launcher experts? Let $A,B$ be real symmetric matrices, and for any $n\in \Bbb N^{+}$, and for all $x,y\in \Bbb R$, we have $$tr(xA+yB)^n=x^ntr(A^n)+y^ntr(B^n).$$  Show that $AB=0$.  My try:since $$(xA+yB)^n=x^nA^n+\binom{n}{1}x^{n-1}A^{n-1}yB+\cdots+\binom{n}{n-1}xA(yB)^{n-1}+y^nB^n$$ so $$tr\left(x^nA^n+\binom{n}{1}x^{n-1}A^{n-1}yB+\cdots+\binom{n}{n-1}xA(yB)^{n-1}+y^nB^n\right)=x^ntr(A^n)+y^ntr(B^n)$$  then  $$tr\left(\binom{n}{1}x^{n-1}A^{n-1}yB+\cdots+\binom{n}{n-1}xA(yB)^{n-1}\right)=0$$ so $$\binom{n}{1}x^{n-1}ytr(A^{n-1}B)+\cdots+\binom{n}{n-1}xy^{n-1}tr(AB^{n-1})=0$$ then I can't  I found this is a nice result, maybe this is an odd problem, and I can't solve it. Thank you. I recently started an account on , and went to add an answer to a question which was protected. I have enough rep on other sites that I have the "Association Bonus", so I was confused as to why I wasn't being allowed to answer the question.     This question is protected to prevent "thanks!", "me too!", or spam answers by new users. To answer it, you must have earned at least 10 reputation on this site.   After re-reading the message and reviewing , I realized that the bonus didn't count as points earned toward that site.  This is a really minor issue, but I think it's worth fixing (not sure if bug or feature).  I believe that users who have enough rep to receive the association bonus should generally already know not to post "thanks!" and "me too!" style answers, so if the message is accurate, users who receive the association bonus should be able to answer protected questions.  If there's another reason to keep users from answering protected questions, such as  claim that:     For protected questions, you are expected to have experience on the target site itself. Experience at other sites is not enough.   then the message should be updated to reflect this.  Option 1:  make protected questions open to anyone who has >10 rep on that site and update the message to read:     This question is protected to prevent "thanks!", "me too!", or spam answers by new users. To answer it, you must have at least 10 reputation on this site.   Option 2:  leave protected questions the way they are, but update the message to read:     This question is protected to prevent "thanks!", "me too!", or spam answers by new users. To answer it, you must have earned at least 10 reputation on this site to show that you have experience on this topic; experience on other StackExchange sites is not enough.   Option 3:  Answer with your own suggestions/improvements to these ideas. How can I prove that all rational numbers are either terminating decimal or repeating decimal numerals? I am trying to figure out how to prove that all rational numbers are either terminating decimal or repeating decimal numerals, but I am having a great difficulty in doing so. Any help will be greatly appreciated. When using the Gmail preview pane lab, fastest way to get a direct link to a conversation? In vanilla Gmail, clicking on a conversation alters the fragment ID in the URL, allowing you to link back to that conversation.  (It opens in its own Gmail interface.)  I am using the preview pane, which is great, except that the URL no longer updates when viewing specific emails, so there appears to be no way to get the link to the currently-viewed conversation.  (The 'open in new window' button doesn't help, since it pulls its contents in on the client side; it isn't a standalone link.)  The only solution I've found is to turn off the preview pane, find the message again in the list, open it, grab the link, go back to the message list, and turn preview pane back on.  That's fairly onerous for something I do often though (to clip Gmail conversations to Evernote, where my GTD setup lives). What are the minimum root filesystem applications that are required to fully boot linux? I define $X_i$ as a random variable that is uniformly distributed between (0,1). What is the expected number of such variables I require to make the sum go just higher than 1.  Thanks Can I use the valid Schengen visa in old passport?