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$\lim_{x\to0^{+}} x \ln x$ without l'Hopital's rule I have a midterm coming up and on the past exams the hard question(s) usually involve some form of $\lim_{x\to0^{+}} x \ln x$. However, we're not allowed to use l'Hopital's rule, on this year's exam anyways.  So how can I evaluate said limit without l'Hopital's rule? I got somewhere with another approach, don't know if it's useful:   $\lim_{x\to0^{+}} x \ln x = \lim_{x\to0^{+}} x^2 \ln (x^2) = L$ $= (\lim_{x\to0^{+}} 2x)(\lim_{x\to0^{+}} x \ln x)$ $= 0 * L$   Then I just need to prove that L is finite/exists (which means it must be 0) Where can I find the location of downloaded .deb files?  I want to copy this folder before I reinstall Ubuntu so I don't have to redownload the packages.  I am running Ubuntu 12.10 32-bit.  How can I do this? Close/minimize/maximize button not appearing I was playing around with compizconfig. I don't remember what exactly I clicked. Since then, the close/minimize buttons and the sidebar vanished. I use 12.10 version. Please help me out. Similar to this question posted in August 2014:       Has the fact that  (as  in The Fires of Pompeii, and  in Torchwood’s Children of Earth season) yet been addressed/explained either in, or out of universe? launch app, capture stdout and stderr in c++ Theoretically if I were able to build some sort of device that let me sit 1 foot away from the surface of the Sun (or any star for that matter) without being vaporized, would a star produce any sort of audible sound at that distance?   From my understanding, sound waves need a medium to propagate through (air, water, etc).   Does this mean that all stars are completely silent (in the audible spectrum of frequencies at least) as they fuse  hydrogen into helium?   I know stars emit radio, xray, infrared, ultraviolet electromagnetic waves, but how about audible (20 Hz to 20Khz) frequencies?   For some reason it seems like this process would produce some sort of sound. Is the topological product $\Pi \{G_\alpha: \alpha < \kappa\} $ a topological group? Replacing some characters in the previous command Electronic visa having Old Passport number Question:   Answer:   The question was closed at 11:57:57 (according to the hover-over-"x-mins-ago" bar) and the answer was posted at 12:16:35. It's a fairly lengthy answer, so it's possible that it was started to be written before it was closed but I swear I've started to answer a question then I got a banner along the top saying "this question has been closed" and the answer was no longer post-able. Infinite Geometric Series Formula Derivation Area enclosed between the curves $y=x^2$ and $y=60-7x$ A continuation of .  I'm fighting a page-limit in a single-column layout and I need to put a Figure and a Table side-by-side and provide them with independent captions. However, the style guide for the publishers (LNCS) wants Figure captions below and Table captions above (probably something to do with ).   =======================================================  If I adapt @lockstep's floatrow example from  accordingly to have a Table caption above ...  \documentclass{article}  \usepackage{floatrow} % Table float box with bottom caption, box width adjusted to content  %% ********************************** %% just adding \captop to original example %% ********************************** \newfloatcommand{capbtabbox}{table}[\captop][\FBwidth]  \usepackage{blindtext}   \begin{document}  \blindtext  \begin{figure} \begin{floatrow} \ffigbox{%   \rule{3cm}{3cm}% }{%   \caption{A figure}% } \capbtabbox{%   \begin{tabular}{cc} \hline   Author &amp; Title \\ \hline   Knuth &amp; The \TeX book \\   Lamport &amp; \LaTeX \\ \hline   Knuth &amp; The \TeX book \\   Lamport &amp; \LaTeX \\ \hline   Knuth &amp; The \TeX book \\   Lamport &amp; \LaTeX \\ \hline   \end{tabular} }{%   \caption{A table}% } \end{floatrow} \end{figure}  \end{document}   =======================================================  The problem becomes clear ...    =======================================================  The floatrow doesn't correctly line up the Table and Caption. I reluctantly tried to use vspace to solve the problem, but it didn't work out.  Any suggestions on how to get these two to align? I'm happy to accept any alignment that ensures that the Table and Figure fit within the same "box".  (A similar-ish question was , but specific for subfig and with a very localised problem it seems.) How are cellphone IP addresses assigned? Is it possible to install Windows 7 alongside Ubuntu and windows 10 dualboot? I installed windows 10 on my laptop in UEFI mode with HDD GPT disk format, then I installed Ubuntu 16.04LTS on another partition. So I have Ubuntu dualboot with Windows 10 now.  I also installed rEFInd (it's like GUI for you to choose between different OSs) because I don't wanna use Grub2 as the default bootloader. Now I want to have Windows 7 too, but when I boot from the USB stick, an error screen showed up saying something like  the windows boot manager is having problems due to a recent hardware change   My system is still working fine so I don't know if the problem came from my system or if the setup I want is impossible. Python __str__ and lists I read a short story (I think, but it might have been a novel), where most races discover a very easy way to travel faster than light at a certain point in their technological development.   What I remember:   The guys in wooden ships bounced around subjugating the people without FTL travel. Earth had never figured out the FTL, and so had poured its effort in a different path, achieving present day technology. The aliens were freaking out about handing the humans FTL travel. The story was told from the point of view of the aliens. I read it in the last 10 years, but there is no telling how old it actually was, although I do remember them mentioning F-18s or F-14s. Working with large numbers in PHP What is this mark over the question When I open a site I see a mark over a question.See screen shot.  When I open the question mark is not remove.It still appear.    is this bug or? Can we use media9 to show a video on a PDF but the video is not embedded to the PDF? I have video tutorials that I want to show in my presentation with beamer class. I don't want the video files get embedded to the PDF because they will make the PDF size very very huge.  If you know how the videos can be played on the HTML with a reference rather than embedding the video file to the HTML file, I want something like this to be applied to my PDF presentation. I just want to reference the video URL from my PDF presentation.   Shortly speaking, can we use media9 to show a video on a PDF but the video is not embedded to the PDF?  Uploading those videos to a web server might be difficult for me because internet connection is very slow and sometimes not available in the presentation room. :-)