Understanding ubuntu
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The sign in the formula for the voltage across the inductor This question is about voltage induced in a inductance.  I know the rate of change of current induces EMF in the inductor. The direction of the induced EMF will be opposite to the change that is causing it. The EMF induced is given by the following formula.  $$V_l = -L \frac{dI}{dt}$$  The negative sign indicates direction of induced emf across the coil is opposite the current change.     In the picture I have drawn current direction and \$V_l\$ direction.  If \$\dfrac{dI}{dt}\$ is postive, \$V_l\$ will be negative according to formula right? Or does the direction of \$V_l\$ has to be reversed?  In many Internet references I found \$V_l = L \dfrac{dI}{dt}\$. Which one is correct?  I hope they reversed \$V_l\$ reference points and removed the negative sign in the formula. Please clarify. Ignoring somebody screws up the avatar list When I ignore a user, the avatar list looks weird.    The blank line beneath the row with the avatar of the ignoree is quite annoying.    I use Google Chrome on OS X.  There was a  tagged  but it still looks weird. My mortgage came up for renewal right at the time in 2009 when UK interest rates hit rock bottom. This was unprecidented, and most financial advice was to take out a fixed-rate mortgage. So I perhaps went overboard and got one for ten years.  Five years on, interest rates haven't moved and I'm losing money on it to the tune of £100 a month. Obviously, this is ongoing: so that decision has cost me about £5000 in real terms so far. It'll come to a lot more by the end of the mortgage, unless interest rates rise.  Being fixed rate, it's been designed so you can't get out early. If I decide to end the mortage, it'll cost me £1,000 per year of the mortgage remaining - which is roughly what I'm losing anyway, so that seems a bad idea.   I can overpay by up to £500 per month. However, doing this doesn't help pay down the mortgage at all: the total is just added up and will cause the mortgage to end early, by a period dependent on the overpayment total.   This seems to me to be a very bad idea because hoping interest rates rise over the next five years is the only hope I have of making good on some of the losses that I've made.   Is this sensible thinking? If so, is there anything at all I can do to try and ameliorate the financial pain this product is causing me? Proving that $\lim_{x \to 0} \frac{f(x)}{|x|}=1$ implies $f$ is not differentiable at $0$. $$\lim_{x \to 0} \frac{f(x)}{|x|}=1$$ Then prove that $f$ is not differentiable at $0$. I was given this assignment and I'm not sure about my proof.. it feels like I'm assuming too much and not explaining with enough detail. Is there anything I need to add to make it sufficient? Assume toward contradiction that $f$ is differentiable at $0$. Then by definition we know that $f$ is continuous at $0$. Therefore $\lim _{x\to 0}f\left(x\right)=f\left(0\right)$ We know that $\lim _{x\to 0}\frac{\left(f\left(x\right)\right)}{\left|x\right|}=1$ Therefore we can conclude $\lim _{x\to 0}\frac{\left(f\left(x\right)\right)}{\left|x\right|}\cdot \left|x\right|=1\cdot 0=0$ But we can also rewrite this as $\lim _{x\to 0}\left(f\left(x\right)\right)\cdot \frac{\left|x\right|}{\left|x\right|}=f\left(0\right)\cdot 1=0$ Therefore $f(0) = 0$. Since $f$ is differentiable at $0$ we have $\lim _{x\to 0}\frac{\left(f\left(x\right)-f\left(0\right)\right)}{x-0}=\lim _{x\to 0}\frac{\left(f\left(x\right)-0\right)}{x}=\lim \:_{x\to \:0}\frac{\left(f\left(x\right)\right)}{x}\cdot \frac{\left|x\right|}{\left|x\right|}=\lim \:\:_{x\to 0}\frac{\left(f\left(x\right)\right)}{\left|x\right|}\cdot \:\frac{\left|x\right|}{x}$ Since the one sided limits of $\frac{f\left(x\right)}{\left|x\right|}$ exist, and are both equal to 1, we have $\lim \:_{x\to 0^+}\frac{\left(f\left(x\right)\right)}{\left|x\right|}\cdot \:\:\frac{\left|x\right|}{x}=\lim \:_{x\to \:0^+}\frac{\left(f\left(x\right)\right)}{x}\cdot \:\:\:\frac{x}{x}=1\cdot 1=1$ $\lim \:_{x\to 0^-}\frac{\left(f\left(x\right)\right)}{\left|x\right|}\cdot \:\:\frac{\left|x\right|}{x}=\lim \:_{x\to \:0^-}\frac{\left(f\left(x\right)\right)}{-x}\cdot \:\:\:\frac{-x}{x}=1\cdot -1=-1$ Since the limit doesn't exist, we have a contradiction to the fact $f$ is differentiable at $0$. Therefore $f$ is not differentiable at 0. Simple property of a valuation on a field Integer solutions for $x^2-y^3 = 23$. As the title stated, I am wondering the integers $x,y$ that satisfy the equation $x^2-y^3 = 23$. TeXnicCenter & Adobe Reader DC How to configure TeXnicCenter to work with Adobe Reader DC? When I building and view current file .tex the following error "Can not execute the command" shows up and the PDF is not generated.    If there are any related post, could help. Thanks a lot! opengl storing multiple indices into indices buffer How do I start with in-camera JPEG settings in Lightroom? I'm a novice shooting in RAW and find that half the time my camera JPEG images come out better than my Lightroom tweaks to RAW files.  So to give myself a better start I'd like to apply the JPEG settings that are applied automatically by the camera to my RAW files in lightroom so that initially my RAW files look exactly like the JPEG files.   How can I do this? What is a word for someone that only does something to benefit them? Take this paragraph for example: I am a follower, not a leader. Hell, I'm not even that good of a follower either, just someone who will do your bidding for the right price. Even then, if it doesn't benefit me -- or put you in debt to me -- I won't do it. How can I upload files asynchronously with jQuery? I would like to upload a file asynchronously with jQuery.     $(document).ready(function () {     $("#uploadbutton").click(function () {         var filename = $("#file").val();          $.ajax({             type: "POST",             url: "addFile.do",             enctype: 'multipart/form-data',             data: {                 file: filename             },             success: function () {                 alert("Data Uploaded: ");             }         });     }); }); &lt;script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/2.2.0/jquery.min.js"&gt;&lt;/script&gt; &lt;span&gt;File&lt;/span&gt; &lt;input type="file" id="file" name="file" size="10"/&gt; &lt;input id="uploadbutton" type="button" value="Upload"/&gt;     Instead of the file being uploaded, I am only getting the filename. What can I do to fix this problem? When an account is deleted, don't auto delete its negatively scored posts on the meta site Meta is different. Negatively scored questions are not always bad questions, and sometimes they have merit and draw good answers, especially discussions.  When an account (in the main site) is deleted, either by self deletion or by a moderator, all questions with score of -1 or less are being deleted regardless of their answers, both in the main and meta site.  Can you please change this behavior so that the questions on the per-site meta will survive and won't be auto-deleted? Looking for a short story about an insect-like alien captured by humans on its own planet This poor creature is taken aboard the spaceship and the humans do not know that it is intelligent.  The alien can repeat what it hears, e,g, "pass the sugar".  It is able to escape at night and it communicates messages to its fellow aliens.  It directs that they turn up the heat of the atmosphere (somehow they can do this) so as to force the humans to leave.  The alien protagonist states that it will die w/ the humans or leave with them. How disk space is used on Android device? How to recover a deleted NTFS partition with data I am on Ubuntu 12.04 64-bits  I accidentally deleted a NTFS 255 GB partition using Gparted, and yes it contains LOTS of important data.  Upon realizing the deletion I haven't yet created any file-system on it. So it still shows Unallocated.    I tried Testdisk , but it shows entire partitions created from the beginning.  This sdb is my secondary drive with Xubuntu and Kubuntu on it. And that 255 GB NTFS  partition was cross platform storage drive.  I am currently in sda with Ubuntu and Win7 in dual boot, which enables me to use it as Safe recovery option rather then Live USB drive.   First ,  should i allocate it to ? file-System for better recovery .  Second , i really need to recover data from this drive so please give me possible  suggestions and proven methods of data recovery.  Third ,does Testdisk requires deleted partition to be allocated for its recovery .  I am currently trying the answer seen here  with Testdisk scanning for partition second time, hoping to recover it.   It looks a duplicate but i can't confirm if the OP got it right. Since my first doubt is to allocate it or not.  If any clarification required please do comment ,i will add it.  Edit: TestDisk deeper search results.      The following partitions can't be recovered:          Partition               Start        End    Size in sectors     &gt;  HPFS - NTFS          22241 107 11 55592   3 27  535777280        FAT32 LBA            274460 158 19 460576 228 16 2989957948  NTFS, 274 GB / 255 GiB &amp; for FAT32 LBA 1530 GB / 1425 GiB How to install Wi-Fi driver for Realtek RTL8821CE on Ubuntu 18.04? The integral $\int_0^\infty \dfrac{x \sin(x)}{x^2+1} dx$ How to calculate: $$\int_0^\infty \frac{x \sin(x)}{x^2+1} dx$$ I thought I should find the integral on the path  $[-R,R] \cup \{Re^{i \phi} : 0 \leq \phi \leq \pi\}$.  I can easily take the residue in $i$ $$  Res_{z=i} \frac{x \sin(x)}{x^2+1}  \quad = \quad \frac{i (e^{ii}-e^{-ii})}{2i}  \quad = \quad \frac{i(\frac1e-e)}{2i} \quad = \quad \frac1{2e}-\frac e2 $$ I know that the integral on $[-R,R]$ will get nearby the real value of $ \frac12\int_0^\infty \frac{x \sin(x)}{x^2+1} dx$. That means that I'm done if I show that the integral on the other part of the path will be small, here is an attempt to do so:  $$ \left|\frac{x \sin(x)}{x^2+1} \right|  \quad \leq \quad  R \cdot \frac{|\sin x|}{R^2-1} $$ I could rewrite $\sin x$ but it becomes nasty. Can you help me with this? How do I get the current date and time in PHP? Which PHP function can return the current date/time? Will my Chinese visa still be valid if I renew my passport? Will my Chinese visa still be valid if I renew my passport? If so how does that work?  I have heard that you can travel with your new passport and just show the old passport with the valid visa when entering China. Has anyone done that? Recently?   I have also been told that you have to get a new visa, which seems somewhat logical but frustrating, especially when my Chinese visa is only a few months old.  My Chinese visa was issued in late Nov 2014 and I heard the rules changed between the US and China. My visa says it's good for 10 years and my US passport expires in 5. Why is $\frac{d^n}{dx^n}(y(x))$ the notation for the $n$th derivative of $y(x)$, instead of $\frac{d^n}{d^nx}(y(x))$? I've always wondered why the numerator is $d^n$ while the denominator is $dx^n$ instead of $d^nx$ like the numerator.  I must be missing something very obvious or fundamental. Is this notation derived from the chain rule in some way?