prove：$\left|x+\frac{1}{x}\right|\geq 2$ prove：  $\left|x+\frac{1}{x}\right|\geq 2$  Can I just use   $\left|\left(\sqrt{x}\right)^2+\left(\frac{1}{\sqrt{x}}\right)^2\right|\geq 2$  and  $\left|\left(\sqrt{-x}\right)^2+\left(\frac{1}{\sqrt{-x}}\right)^2\right|\geq 2$?
How to prove this inequality $ x + \frac{1}{x} \geq 2 $ I was asked to prove that:   $$x + \frac{1}{x}\geqslant 2$$  for all values of $ x &gt; 0 $  I tried substituting random numbers into $x$ and I did get the answer greater than $2$. But I have a feeling that this is an unprofessional way of proving this. So how do I prove this inequality?
How to get ongoing notifications of unread texts? One of my family members texts me at night when they are having nightmares. I want to know when they text me at 4 am instead of sleeping through it.  Is there a way to make text notifications keep going off until read? Is there a reason I would not add /usr/local/sbin, /usr/sbin, /sbin to my path on Debian? Installing PHP 5.3 in Ubuntu 14.04 How to remove feeds from WordPress totally? I want to completely remove feeds from WordPress. I am using this little function from    /** * disable feed */ function fb_disable_feed() { wp_die( __('No feed available,please visit our &lt;a href="'. get_bloginfo('url') .'"&gt;homepage&lt;/a&gt;!') ); } add_action('do_feed', 'fb_disable_feed', 1); add_action('do_feed_rdf', 'fb_disable_feed', 1); add_action('do_feed_rss', 'fb_disable_feed', 1); add_action('do_feed_rss2', 'fb_disable_feed', 1); add_action('do_feed_atom', 'fb_disable_feed', 1);   Still there is tons of transient options.. like _transient_feed_mod or _transient_timeout_feed_mod  How can i completely remove feeds from WordPress? Word: how to show hidden ribbon tabs? How can I control which tabs are available to be opened in the MS Word 2010 ribbon?  Under Word Options > Customize Ribbon > Main Tabs there are several groups checked (Blog Post, Insert (Blog Post), Outlining, Background Removal), but they don't appear on the ribbon even though there is space for them. How is one supposed to turn them on or get to them?  The one in particular I'm after today is the Blog Post tab, which I know I can get to in a round about way via File > New > Blog Post Template. However I don't want a new post, rather an old one, which means File > New > Blog Post Template > Open existing > [select from list] > [close new blog post window] > [slap No I don't to save darn it]. Extra work for nothing is irritating; how do I get Blog Post (or Outlining or ...) to show up in that nice empty space next to AddIns? Prove that the multiplicative inverse of $a$ modulo $m$ exists if and only if $a$ and $m$ are coprime.  Can someone help me with this? Is it possible to delete multiple elements from a list at the same time? If I want to delete elements at index 0 and 2, and try something like del somelist[0], followed by del somelist[2], the second statement will actually delete somelist[3].  I suppose I could always delete the higher numbered elements first but I'm hoping there is a better way. How to style text in hyperref \url? I want to set color, font and similar style attributes for the text in a \url from the hyperref package. How do I go about doing it? All I have found are . I want to because I am using ttf fonts for my texts and I want my urls to be in that ttf and not the default (typewriter font?) that the hyperref package gives me. I started with just trying to get it in italics but didn't even succeed with that:  \documentclass{memoir} \usepackage{hyperref} \begin{document} Lala \url{\itshape www.example.com}. \end{document}     I am guessing there is some hook or something but I just can't find it. Maybe I have gone blind? How to use a proxy on the command line? I can set my proxy username and password along with proxy settings in the proxy ui but these settings do not work on the command line. How can I use apps such as wget &amp; ping on the command line with a proxy?  Example Details:   username: 1234 pass: linux proxy: proxy port: 8080 Am I going to have trouble flying with a reversed name on the ticket? I'm flying to Peru with my girlfriend next week and I realized that her name is incorrect on the reservation.  Instead of Sally Marie Jones it's Jones Marie Sally.  We're flying into Houston, then Lima, and in Lima we switch airlines for our flight to Cajamarca.  I booked the ticket with Orbitz who made the reservation with United. United booked the flight with LAN air, the Peruvian airline.  Both companies say that they are unable to change the name because of TSA restrictions not allowing a name change. I asked if I could just cancel and re-book, but United said they could not do this because there are multiple airlines involved.  A note has been attached to the reservation explaining the issue, and the United rep said that they would be able to print her boarding pass with the correct name. However, he said there are no guarantees that she'll be able to fly because although the boarding pass will be correct, the ticket will still have the reversed name.  I was prepared to just take the chance that it will all work out, seeing how it's really obvious the name is just backwards, but with recent events I'm worried that US airport security is going to be extra strict for the next little while.  Is this something I need to worry about, or are chances good that this will work out fine?  The United rep said there's a chance we could cancel the United flights and get a new ticket with the correct name for no cost, but we'd have to pay for new tickets within Peru ($500 out of the total $1300 ticket cost). I'd rather not do this unless there's a reasonable chance we'll have trouble at the airport. How can I make a div not larger than its contents? I have a layout similar to:  &lt;div&gt;     &lt;table&gt;     &lt;/table&gt; &lt;/div&gt;   I would like for the div to only expand to as wide as my table becomes. Import pdf form in latex with filled in text How to record both screen and sound with Quicktime on El Capitan? I'm trying to record both what's happening on screen and the audio being played by the applications. To my surprise, QuickTime did not record the sound. I believe it worked before in previous OS X releases, but that is not something that I use often so I have not bothered to try earlier.  What is the current situation on El Capitan ? Have I messed with something that prevents QuickTime from capturing the sound, or has it never worked ?  Here is my view of Quick Time  / New Screen Recording on a Mac Mini:   On my Macbook Pro, I have the option select None or Internal Microphone. Internal microphone actually records the speakers of the Mac Book as heard from its own microphone, which obviously sounds terrible.  This is a MacMini 7,1 (late 2014) and there is nothing in Input Sources. Trackpad not working after update to Ubuntu 14.10 on Dell Inspiron 15R Do I need to reboot my HTC Desire periodically? I expect to be working on a web application within the next several months and I'd like to "shoehorn" a Spanish language version of the site. If a large enough number of Spanish language users begin using the site we'll likely hire a professional translator (or at least recruit someone who actually knows the language), but in the meantime is there a good cheat sheet I can use for common UX keywords, like "OK", "Submit", "Cancel", "Delete" and "Save"?  I know I could use an online translator, but I'm concerned the translator would not pick up on context (thus giving me a Spanish word meaning something closer to "Take" for "Accept" or "Surrender" for "Submit", etc.)  I'm not looking for a 100% solution, just something to give me the bulk of the keywords until there's enough reason to hire a real translator. This site will be in a beta development phase for a long time, I think, so we're not expecting a huge user base to start things off. How can I align a multiple-line footnote text right to the footnote mark? How can I have the following "footnote layout"?  Some Text Some Text Some Text Some Text² Some Text   2 FOOTNOTETEXT FOOTNOTETEXT FOOTNOTETEXT FOOTNOTETEXT FOOTNOTETEXT   FOOTNOTETEXT FOOTNOTETEXT FOOTNOTETEXT FOOTNOTETEXT FOOTNOTETEXT   My problem is that the footnote text starting with the second line is too far left.  \documentclass{article} \usepackage{blindtext}  \begin{document}     \blindtext\footnote{\blindtext} \end{document} When the phrase is used as an object, why so many native speakers are saying "you and I" instead of "you and me"? I'm not a native speaker but I thought "you and me" is correct. Not sure if this falls into the same category, but "Just between you and me" sounds more natural than "Just between you and I". unzip error "End-of-central-directory signature not found" I try to unzip a zip file, but got an error:  $ unzip COCR2_100.zip  Archive:  COCR2_100.zip   End-of-central-directory signature not found.  Either this file is not   a zipfile, or it constitutes one disk of a multi-part archive.  In the   latter case the central directory and zipfile comment will be found on   the last disk(s) of this archive. note:  COCR2_100.zip may be a plain executable, not an archive unzip:  cannot find zipfile directory in one of COCR2_100.zip or         COCR2_100.zip.zip, and cannot find COCR2_100.zip.ZIP, period.   I googled but didn't find a solution. I was wondering why it is and how I should fix it? Thanks!  The zip file can be downloaded from . It is an application, and here is its website .  My OS is 10.10. What are watched tags and ignored tags? How do they work? What are tag subscriptions? What are interesting tags? On Stack Overflow, the content of the main page question list appears to be influenced by watched and ignored tags. How does that work?   For more information, see &quot;&quot; in the .