If $f$ is a real-valued function that is integrable over $\mathbb{R}$, does it imply that  $$f(x) \to 0 \text{ as } |x| \to \infty?  $$  When I consider, for simplicity, positive function $f$ which is integrable, it seems to me that the finiteness of the "the area under the curve" over the whole line implies that $f$ must decay eventually. But is it true for general integrable functions?
I'm trying to prove  the following claim:     If $f$ is continuous  and $\displaystyle\int_a^\infty |f(x)|\;dx$ is finite then $\lim\limits_{ x \to \infty } f(x)=0$.   Here the counter example of all these sine functions won't do, since  their infinite integral does not converge absolutely.   Any hints for a proof?
How do I install Ubuntu alongside a pre-installed Windows with UEFI? How to make cmd correctly display arabic script? Anti-virus comparison for Mac OS X This is not a "I use OS X, do I need Anti-Virus?" question.    I am looking at comparison and user opinion of existing AV products. I know I can avoid most (if not all) threats by being careful on the sites I visit, and the emails I download. But I need an anti-virus, for a variety of reasons - mostly to prevent my Mac as a carrier for viruses. (Many friends' USB drives turn out to be infected).  I was looking for the "Best" of the anti virus software out there.  I am looking prominently at anti-virus. "Internet Security" and the like are not important, and would try to avoid them if it would save money or not make my mac slower.  By "Best" I mean the best combination of detect-rate (or whatever that is called) and performance.  I don't intend to run it always in the background. Maybe I would do a onetime scan of my system and hard drives, and then it would be mostly on a need basis, especially on USB drives/portable hard disks of friends. So primary objective: High Detect rate  I have used  and  (got this with one of those software bundles sometime before, not the latest version) and had problems with both. Both sometimes hog my CPU, and somehow "lock" my USB drives preventing me from Ejecting it (I had to force eject them or just pull them off from the port) (thought off late Norton seemed a little better)  Ok, thats a long one. But my question is simple: What anti-virus do you recommend for the Mac?  Thanks. Lightning Cancel Enqueued Server Side Action In the previous version the logout button is under your username, which it can be found by clicking the down arrow. However, in the new version, after a couple minutes of searching, it is under the "site-switcher" button:        This is really illogical since the logout button is usually under your username, including Google and Yahoo! services.  I suggest bringing back the  which will definitely benefit new users and even old users. I'm having problems using the UV mapping in blender 2.67. Specifically, I am trying to unwrap a really simple mesh, but the UV map is still giving me a net where some of the boxes are completely out of proportion to the others, which causes the texture to stretch horribly. Here is a picture to illustrate:    The mesh only has those three faces you can see in the picture, and the single seam on the front corner. It's a trivially simple mesh, so I really don't understand why the two side faces are being stretched in the UV map to be the same size as the top face. I've tried clicking the average islands scale button as suggested by some of the answers to other questions but that has no effect. It's frustrating because it seems so simple.  Hopefully someone can show me the presumably simple mistake I am making!  Edit: Just to make this clearer, I have already added a seam as the first answer suggests i do. Hopefully this picture will make that clearer, the yellow arrow is pointing to the edge i seamed. The mesh is only three faces so should only need this single seam. The image shows the mesh from infront and behind/underneath so it should make more sense.    Double Edit: One more picture for clarity on the seam issue. The mesh is unfolding correctly, it is just the scale of the unfolded map that is incorrect (in relation to one another) When Deadpool is in the hallway talking      he makes a joke about Fox springing for a few more X-Men and the camera pans to show Beast closing the door to get rid of the noise.   Who else was in the room? Beamer: How to Disable `\pause` Temporarily Is there a difference between foo(void) and foo() in C++ or C? Consider these two function definitions:  void foo() { }  void foo(void) { }   Is there any difference between these two? If not, why is the void argument there? Aesthetic reasons? How to get the last value of an ArrayList Every power series is the Taylor series of some $C^{\infty}$ function For which $x$ exists sum $1 + 2 + 3 + \ldots + n$, where $n &gt; 3$, which has notation $xxx\ldots x$?   In other words, I am looking for a sum of natural numbers which gives a result which has all same digits, e.g. $5555555$ or $22222222222222222$, or whatever else.  How to find this series and how to proof it for all possible series?  I have found the following examples:   $1 + 2 + 3 + \ldots + 10 = 55$ $1 + 2 + 3 + \ldots + 11 = 66$ $1 + 2 + 3 + \ldots + 36 = 666$     And what about next series which ends with (different) repeating $x$? Hot to find and proof it? How do I find out which DOM element has the focus? Vehicles required/allowed in weigh stations on US interstates Why do I get a black rectangle instead of my external picture? I write some of my network notes in TeX. I wanted to make a table, and inside it insert an image:   .   I wrote a document:  \documentclass{article} \usepackage[demo]{graphicx} \usepackage{booktabs} \usepackage{array}  \begin{document} \begin{tabular}{m{3cm}m{3cm}m{5cm}} \toprule Configuration for ... &amp; Commands &amp; Topology\\ \midrule PPP: CHAP, PAP &amp; \#sh int se 0/0/0  &amp; \includegraphics[width=4cm, height=4cm]{chappap.png}\\  &amp; &amp; \\ \bottomrule \end{tabular} \end{document}   But instead of my network topology image, I see only this: .   I don't know what is wrong, cause my image is 100% in the same dir, as my *.tex file.  EDIT:  Changed my code as @Jubobs suggested, now everything is as I wanted:  \documentclass{article}     \usepackage{graphicx}     \usepackage{booktabs}     \usepackage{array}      \begin{document}     \begin{tabular}{m{3cm}m{3cm}m{5cm}}     \toprule     Configuration for ... &amp; Commands &amp; Topology\\     \midrule     PPP: CHAP, PAP &amp; \#sh int se 0/0/0  &amp; \includegraphics[width=4cm, height=4cm]{chappap.png}\\      &amp; &amp; \\     \bottomrule     \end{tabular}     \end{document} How to retrieve GET parameters from JavaScript $(n+1)$th prime $p_{n+1}$ less than or equal to $p_1p_2\dots p_n+1$ On all of the other SOFU sites a downvote means The question is unclear or not useful.  However, here on meta, a downvote has become a sign of I don't agree with the question, suggestion, feature request, bug, etc. being described in the question.   What does a downvote on Meta really mean? What other reasons do people downvote on Meta? Why is it okay for meta to redefine the meaning of the downvote?  The tooltips and instructions are all the same here on meta.   Note: I'm not saying I disagree with the practice, just curious. How to test if these two samples are from the same distribution? (These are tweets located near some tourist attractions.     If yes, is there a simple implementation in Python? What does the typical workflow of a journal look like?