How to prove $\int_0^{\infty} \frac{\sin x}{x} \, dx = \frac{\pi}{2}$
Evaluating the integral $\int_0^\infty \frac{\sin x} x \,\mathrm dx = \frac \pi 2$?
Proof of upper-tail inequality for standard normal distribution $X \sim \mathcal{N}(0,1)$, then to show that for $x &gt; 0$, $$ \mathbb{P}(X&gt;x) \leq \frac{\exp(-x^2/2)}{x \sqrt{2 \pi}} \&gt;. $$ I'm trying to make a conditional formatting rule in Google Spreadsheet that would highlight a row green based on text in multiple cells.   If cells L2, M2, and N2 = APPROVED; and cell O2 = X; then row 2 = highlighted green. I need to install a new TeX/LaTeX/ConTeXt package on my computer.  I'm running Ubuntu/Fedora/Slackware/Some-Version-Of Linux.  What are the possible ways to do this?    Note:&nbsp;&nbsp; We get a number of questions that essentially reduce to this one; it was felt a good idea to have one question-and-answer that can cover all the standard methods.  See  for the discussion.  The question-and-answer are CW so that more information can be easily added.  If you have information to add, please do so.  If you are unsure, leave a comment here or (preferably) in .  Comments on the question and answer will be periodically removed to ensure that the information is clear. Make bash exit != 0 when called by AWK and interrupted with ^C I'm having an issue with the following piece of (G)AWK script:  do {     ... } while (system("sleep 10"))   My intention is to break the loop when the user presses ^C during the sleep, but it's not working.  I believe the problem is that Bash exits with 0 when interrupted with ^C, at least when it's executed by AWK's system():  $ awk 'BEGIN { print "\n" system("sleep 2") }' (let the sleep complete) 0      $ awk 'BEGIN { print "\n" system("sleep 2") }' ^C 0   Why is it so?   Is this a bug in Bash or in (G)AWK?  Is there a simple solution that doesn't involve complicated Bash-specific syntax like trap?  The best I could come up with is this:  do {     ... } while (42 == system("sleep 10 &amp;&amp; exit 42"))   which still looks like a kludge to me. brute force password guessing on SSH server isn't going to work? I'm running an SSH server on my personal computer. The log had many people(or bots?) repeatedly trying to log in to my server (that is before I changed the default port), which made me a little freaked out. I was worried about their dictionary attacks or brute force password guessing.  But then if you type wrong password (or wrong username), the server waits for about 2 seconds before it asks for password again. So an attacker can try one password per 2 seconds. So I concluded that these attacks aren't that great a threat (as long as your password does not consist of dictionary words.) Am I correct? Why are there hexagonal holes in my donut? I'm currently making a donut using blender gurus tutorial. I have no idea why, but there are holes in my icing. Does anyone know what could be causing it? Thanks for any help. How was the bank robbery completed? In Now You See Me, when Morgan Freeman explains to the detective on how the Four Horseman robbed the bank, he mentions that they replaced the real money (while in the secured transport truck) with flash paper.  This does not explain how the paper in the bank got ignited, and no ignition/stimulator left in the scene as evidence.  Who/What/When ignited the flash paper in the bank on time?   There had to be some timer/delay mechanism on the platform, or something similar - but in the frames we see - there is nothing. Story ID: Boy who is stuck at 5 years old with robot nanny Here's what I remember:  The boy is 5 years old, and has been for some time, because there's a bit in which he recalls turning 5 (celebrating his 5th birthday) many different times  There's a robot nanny in the apartment with him that he learned to disable so that he can hang out with the girl, who he isn't supposed to know. (In my mind the nanny bears somewhat of a resemblance to Muthr from the Wondla series... however I definitely read this story well before reading Wondla)  There's a neighbor girl who teaches him to read (I think she's like 9), and when they first meet she asks how old he is (5 is the last age at which growth/development can be successfully (and safely?) suspended) and he lies, saying that he's 6, but doesn't know why he does.  When a child whose aging process has been stopped learns how to read, they begin aging normally again, so the parents don't want them to learn to read.  The children who have stopped aging are kept apart from other children who grow normally-- they have separate playgrounds and the like  The injection/serum used to halt the aging process was developed by a scientist, who when he first shared his findings had a 5 year old son and injected him, then told the onlookers/potential buyers/other parents to come back in 20(?) years. When they did, their children were adults and no longer needed them or were ungrateful layabouts, and the scientist's son was still 5 years old, cute, needy, etc.  The main character has a discussion about how he wants to turn 6 with his parents and they agree but only because he's already learned to read and it's irreversible.  It's kinda dark and emphasizes the need that parents have to feel wanted. Please help! I remember it so vividly and I'd love to read it again! How to Regex search/replace only first occurrence in a string in .NET? It seems the .NET Regex.Replace method automatically replaces all matching occurrences.  I could provide a MatchEvaluator delegate that returns the matched string after the first replacement, rendering no change, but that sounds very inefficient to me.  What is the most efficient way to stop after the first replacement? Evaluate the infinite product $$\lim_{ n\rightarrow\infty }\prod_{k=2}^{n}\left ( 1-\frac{1}{k^2} \right ).$$  I can't see anything in this limit , so help me please. JavaScript private methods To make a JavaScript class with a public method I'd do something like:  function Restaurant() {}  Restaurant.prototype.buy_food = function(){    // something here }  Restaurant.prototype.use_restroom = function(){    // something here }   That way users of my class can:  var restaurant = new Restaurant(); restaurant.buy_food(); restaurant.use_restroom();   How do I create a private method that can be called by the buy_food and use_restroom methods but not externally by users of the class?  In other words, I want my method implementation to be able to do:  Restaurant.prototype.use_restroom = function() {    this.private_stuff(); }   But this shouldn't work:  var r = new Restaurant(); r.private_stuff();   How do I define private_stuff as a private method so both of these hold true?  I've read  a few times but it doesn't seem like "private" methods can be called by public methods and "privileged" methods can be called externally. What is the difference between French and British cuts of beef? What is the difference between French and British cuts of beef?   I am told they just butcher the animals dfferently. Certainly the cuts don't seem the same. For example is faux fillet really exactly the same as British sirloin and is entrecôte really the same as rib steak?  Here is a picture of British beef cuts. I did a fresh install of Ubuntu 16.04. /dev/md1 contains an ext4 filesystem that is mounted at /:  /dev/md1 on / type ext4 (rw,relatime,data=ordered)   Now I want to set the automatic filesystem check interval to one month, but I'm getting a strange error that I find no useful information about:  &gt; tune2fs -i 1m /dev/md1 tune2fs 1.42.13 (17-May-2015) tune2fs: Filesystem has unsupported read-only feature(s) while trying to open /dev/md1 Couldn't find valid filesystem superblock.   Rebooting didn't help. On another machine running Ubuntu 12.04, the same command works like a charm.  Does anyone have an idea what's wrong?  The command tune2fs -l /dev/md1 works fine, by the way. Here is its output:  tune2fs 1.42.13 (17-May-2015) Filesystem volume name:   &lt;none&gt; Last mounted on:          / Filesystem UUID:          38366a40-bbe1-476b-acfe-d271be6335eb Filesystem magic number:  0xEF53 Filesystem revision #:    1 (dynamic) Filesystem features:      has_journal ext_attr resize_inode dir_index filetype needs_recovery extent 64bit flex_bg sparse_super large_file huge_file dir_nlink extra_isize metadata_csum Filesystem flags:         signed_directory_hash Default mount options:    user_xattr acl Filesystem state:         clean Errors behavior:          Continue Filesystem OS type:       Linux Inode count:              8380416 Block count:              33521664 Reserved block count:     1676083 Free blocks:              32419430 Free inodes:              8312762 First block:              0 Block size:               4096 Fragment size:            4096 Group descriptor size:    64 Reserved GDT blocks:      1024 Blocks per group:         32768 Fragments per group:      32768 Inodes per group:         8192 Inode blocks per group:   512 Flex block group size:    16 Filesystem created:       Thu May 31 10:01:27 2018 Last mount time:          Thu May 31 10:49:41 2018 Last write time:          Thu May 31 10:15:14 2018 Mount count:              7 Maximum mount count:      -1 Last checked:             Thu May 31 10:01:27 2018 Check interval:           0 (&lt;none&gt;) Lifetime writes:          5782 MB Reserved blocks uid:      0 (user root) Reserved blocks gid:      0 (group root) First inode:              11 Inode size:               256 Required extra isize:     32 Desired extra isize:      32 Journal inode:            8 First orphan inode:       4325378 Default directory hash:   half_md4 Directory Hash Seed:      9d55d989-2c2b-4ad8-a29e-53c8798ec68e Journal backup:           inode blocks Checksum:                 0x3d9f8d23 So you are camping (please excuse the MMO jargon, sometimes I just can't help myself) your own particular corner of Stack Overflow, hoping for a couple of upvotes before bed.  It's freezing cold and you can't quite drag yourself across the room to grab the little blow heater, because that would mean leaving the almost adequate warmth of your laptop.  A completely objective question pops up, to which you absolutely know the answer.  Riding the surge of adrenaline, you spend the next twenty minutes typing like a madman. Desperate to beat the other lunatics that loiter in your tag of choice.  You beat them to the punch and enter a superlative answer, code samples, examples and maybe some ironic humour. You are flushed with your own awesomeness.  You go to bed. Satisfied you have garnered a couple of points of virtual self validation. You look forward to the flush of pleasure in the morning when you see your account bumped ever closer (yet never close enough) to that shining example of Skeetness.    Yet, the next morning, no such flush occurs.  Your answer sits in prime position for some questioner love and none eventuates.  You might get a couple of upvotes from some sympathetic SO compatriot, but the ultimate (I'll try to avoid any unsavory metaphors here)  satisfaction of accepted answer is denied you.    So my question. How you react to this kind of situation?   Catch yourself monitoring the questioner's account waiting for them to log on and then breaking nearby inanimate objects when your answer continues to be ignored. Panic that the questioner might delete their account, leaving your beloved question to evaporate in a puff of uninterest.  Wondering if it was something you said and answering some other of the questioner's queries in the hope of redeeming yourself in their fickle eyes.   I have seen a few examples of this type of frustration on Twitter and wondered how the hardcore Stack Overflow community dealt with this type of rejection. From time to time certain chat rooms (JavaScript and probably PHP, too) attract the attention of a fellow help vampire who thinks he can start sucking from the people in there.  Often their message end up being flagged as offensive (and those flags are likely to be validated, too, because people are annoyed by such behaviour) but it's kind of an inappropriate use of those flags.  I'm proposing a new chat flag type, which is especially meant for help vampires. Flagging it would present the flag to 10k users and owners of the room where the flag originated (no matter how much rep they have). When the flag is validated it would cause messages from this user to be shown with a low opacity for maybe three hours. It could also notify the user that help vampirism is a bad thing and that he needs to improve his behaviour.  Repeated flags of this type - obviously with some time in between in case multiple message which are really part of the same conversation are flagged - should then result in a temporary ban from the room where the messages got flagged. If that doesn't help the next step would probably be a temporary ban from all chat rooms.    For clarification, I'm not talking about the quick "this line doesn't work, why?" stuff but the kind of help vampires who get cocky even though they just got e.g. a link to a SO question which has a perfectly fine and fitting answer. Because hey, you didn't give them teh codez! Black screen on boot after AMDGPU-Pro install (16.04) I have been having some screen freezing issues on my new Ubuntu 16.04 system, and have been in the troubleshooting process for this issue. I thought it was a graphics driver problem, as I am running an AMD R9 380x card which was supposed to be fully supported by the open-source AMDGPU driver preinstalled with 16.04, but after looking around online, many people seem to have issues with. I thought the answer would be to install the recently released AMDGPU-Pro driver , following the instructions from . However, when I reboot I am getting a black screen. Is there an easy way to revert my changes back? My machine was semi-functional with the freezing issue but now with no video at all is useless to me. How to proceed? How do I get the last column text to be at the bottom of the row?  That is I want the XXX to be aligned with the line containing the arrow. I tried playing around with \multirow{3}{-3ex}{XXX}, but obviously I don't understand \multirow. Code: \documentclass{article} \usepackage{tabularx} \usepackage{booktabs} \usepackage{multirow}  \begin{document}     \begin{tabularx}{\linewidth}[t]{l X p{1.3cm}}         &amp; Header &amp; Title \\\cmidrule(lr){2-2}\cmidrule(lr){3-3}         a. &amp; Some text text text text text text text text text text text text text text              text text text text text text text text text text              Want XXX on this line $\rightarrow$%          &amp; XXX\\     \end{tabularx} \end{document} How do you Set Custom Time in Ubuntu? Female main character in an ice world earning gems/runes Here's what I remember:   The main character's female (99% sure) There is one part where she has to cross a big tundra and she has to kill a big ice creature The kids in the story go to a school-like place where they train for something. I'm pretty sure they earn gems or runes or something like that There's one part where the main character has to play a piece of music perfectly to earn her gem/rune thing It's definitely a series; young-adult (I read them in middle school)   Thanks! When do I need to invoke \phantomsection?