If $ a &gt; 1 $, then      $$ \lim_{x \to \infty} \frac{a^x}{x} = \infty. $$   Above one can find the limit which is to be shown. Any tips? The epsilon/delta method, taylor series, definition of a derivative, etc, are not accepted as it is viewed as circular reasoning. Anyways, I really do not know how start but I guess that I should use the squeeze theorem someway down the track.
In other words, how to prove:  For all real constants $a$ and $b$ such that $a &gt; 1$, $$\lim_{n\to\infty}\frac{n^b}{a^n} = 0$$  I know the definition of limit but I feel that it's not enough to prove this theorem.
Why can't variables be declared in a switch statement? I've always wondered this - why can't you declare variables after a case label in a switch statement?  In C++ you can declare variables pretty much anywhere (and declaring them close to first use is obviously a good thing) but the following still won't work:  switch (val)   {   case VAL:     // This won't work   int newVal = 42;     break; case ANOTHER_VAL:     ...   break; }     The above gives me the following error (MSC):     initialization of 'newVal' is skipped by 'case' label   This seems to be a limitation in other languages too.  Why is this such a problem? "Same as I do" or "same as I have" She has the same book as I have.  Isn't it supposed to be She has the same book as I do?  But I often hear the former.  Why? I'm starting out in Visual C++ and I'd like to know how to keep the console window.  For instance this would be a typical "hello world" application:   int _tmain(int argc, _TCHAR* argv[]) {     cout &lt;&lt; "Hello World";     return 0; }   What's the line I'm missing? Google Chrome is not starting I've just installed Ubuntu 16.04 LTS on dual boot. I've looked for many solutions and tried them all but Chrome never starts; the logo appears on the left but no window opens.  I downloaded the deb file on google chrome website and installed it through Ubuntu Software, but it doesn't start.   I have tried installing it through the command line with   sudo dpkg -i --force-depends google-chrome-stable_current_amd64.deb sudo apt-get install -f   I have checked with uname -a and my system is 64 bit. I have also tried gdebi with the same result.   My repository universe is up to date.  I only have one display in settings>displays> so I can't turn off built-in display nor check the mirror display (I read it could be the problem as I also have a graphic card but it seems it is not in my case).  Here is what I get in the command line when I try to run Chrome from it ( the message is the same, whatever the method I used to install Chrome):  ~$ google-chrome [11831:11831:1122/114854.195473:ERROR:process_singleton_posix.cc(433)] readlink failed: Permission denied (13) [11831:11831:1122/114854.195493:ERROR:process_singleton_posix.cc(256)] readlink(/home/basil/.config/google-chrome/SingletonLock) failed: Permission denied (13) [11831:11831:1122/114854.195508:ERROR:process_singleton_posix.cc(256)] readlink(/home/basil/.config/google-chrome/SingletonLock) failed: Permission denied (13) [11831:11831:1122/114854.195515:ERROR:process_singleton_posix.cc(280)] Failed to create /home/basil/.config/google-chrome/SingletonLock: Permission denied (13) [11831:11831:1122/114854.195538:ERROR:process_singleton_posix.cc(433)] readlink failed: Permission denied (13) [11831:11831:1122/114854.195564:ERROR:process_singleton_posix.cc(256)] readlink(/home/basil/.config/google-chrome/SingletonLock) failed: Permission denied (13) [11831:11831:1122/114854.195622:ERROR:chrome_browser_main.cc(1498)] Failed to create a ProcessSingleton for your profile directory. This means that running multiple instances would start multiple browser processes rather than opening a new window in the existing process. Aborting now to avoid profile corruption. [11831:11868:1122/114854.209297:ERROR:browser_gpu_channel_host_factory.cc(108)] Failed to launch GPU process.   Any new approach will be much appreciated How is hotness score calculated at larger sites? To start with, I am aware that hot questions from larger sites are somehow "penalized" and :     This is designed to ensure that a single site doesn't dominate the list, and that users see a good sampling of questions that are likely to interest them throughout the network...   I would like to understand how is hotness score really calculated at these sites. The reason why I ask is that per my observations, this seems to be quite different than is documented in the . Specifically, I would like to understand the difference in the impact of answer(s) score and aging factor.  Regarding impact of answers score, my observations of hot questions from smaller sites appear to be in agreement with known formula: (MIN(AnswerCount, 10) * QScore) / 5 + AnswerScore. For example, a question with low score (+1, +2) can get into hot list if it has got answer(s) with sufficiently high score.  At larger sites, this doesn't seem to be the case. Say, it looks like Stack Overflow questions just don't enter hot list until they reach certain score (+6,+7), no matter how many answers are there and how high is their score.  Does system simply totally ignore answers until question reaches certain score?  Another thing I noticed is that questions seem to age away from the hot list 2-3 times faster than ones from smaller sites (having comparable question and answers scores). Granted, this is harder to track and I am not yet sure if I figured that correctly. Do larger sites questions age away faster than those from smaller sites?    For those interested, here is a (partial) list of example questions I studied before asking this: , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , .  Although above examples are only from Stack Overflow, my question isn't (I only used it as an example of a large site in my studies). I would like to understand if hot questions from other larger sites are handled in a similar way. Prove $\frac{1+a^{2}}{1+b+c^{2}} +\frac{1+b^{2}}{1+c+a^{2}} +\frac{1+c^{2}}{1+a+b^{2}} \geq 2$ For positive integers Numbers  $a, b, c $ prove that  $$\frac{1+a^{2}}{1+b+c^{2}} +\frac{1+b^{2}}{1+c+a^{2}} +\frac{1+c^{2}}{1+a+b^{2}} \geq  2$$ This inequality above take long time to prove it and still couldn't complete it.  How I can prove this inequality?  Any hint will help. Thanks Do magic item spells require concentration? Do magic items that cast a magic effect such as a ring of invisibility require the user to maintain concentration as if they had cast the spell?  Is this also the case if the item casting the spell is an artifact?   If the item is intelligent can it concentrate on the spell? Shortcode display outside the div I have created a shortcode that retrives and displays a form.The content of the attribute in HTML.   function check_my_login( $atts)     {          return '&lt;form action="" name="" method="post" enctype="multipart/form-data"&gt;                &lt;div class="form-group"&gt;                     &lt;label for="description"&gt;Project Description&lt;/label&gt;                     &lt;textarea name="p_description" placeholder="Project Description" class="form-control"&gt;&lt;?php if (isset($_POST['p_description']) &amp;&amp; $_POST['p_description'] != '') echo $_POST['p_description'] ?&gt;&lt;/textarea&gt;                 &lt;/div&gt;                  &lt;div class="form-group"&gt;                     &lt;label&gt;Project Attachment&lt;/label&gt;                     &lt;input type="file" name="p_attachment"&gt;                 &lt;/div&gt; &lt;/form&gt;';     }     add_shortcode( 'kentaUser', 'check_my_login' );   Now use this shortcode inside the Post/page.   Like this    &lt;div class='manage_page'&gt;[kentaUser]&lt;/div&gt;  But my shortcode content display out side the div.Display upper side in post/page content.  &lt;div class='manage_page'&gt;&lt;/div&gt;    Any one short out this problem. Pseudo-terminal message in script Is there a correct resistance value for I2C pull-up resistors? biblatex - issue number of journal in date I am building a bibliography using biblatex and biber (\usepackage[backend=biber,minnames=2,backref,firstinits,sortcites]{biblatex}) with a lot of cited papers. Therefore I often have the case of a journal name, volume, issue, month and year, all necessary.   Now the strange thing is, if I have a bibitem such as:  @article{item,   title = {Some Nice Scientific Title},   author = {Doe, Jane},   journal = {Important Journal},   volume = {50},   issue = {20},   pages = {1877--1879},   year = {1984},   month = {Jun},   publisher = {Important Society},   doi = {00.0000} }   the bibliography looks like this:    Can you spot it? The issue number 20 is in the brackets with the date. Now it looks like it is the day in the date.  So, how do I get around this?  Here's the full MWE:  \documentclass{scrartcl}  \usepackage[backend=biber,minnames=2,backref,firstinits,sortcites]{biblatex}  \usepackage{filecontents} \begin{filecontents}{item.bib}   @article{item,     title = {Some Nice Scientific Title},     author = {Doe, Jane},     journal = {Important Journal},     volume = {50},     issue = {20},     pages = {1877--1879},     year = {1984},     month = {Jun},     publisher = {Important Society},     doi = {00.0000}   } \end{filecontents}  \addbibresource{item.bib}  \begin{document}  \printbibliography[title = {References},heading=bibintoc] \nocite{*}  \end{document} vertical alignment of a turned cell I know using turn command and a sample code like this:  \usepackage{rotating}  \begin{turn}{90} Supervised Learning \end{turn}}   we can rotate a text inside a cell, however, I couldn't find a way to vertically center this rotated text. Any suggestions is appreciated.  Here is the sample MWE:  \begin{table}[]     \centering     \begin{tabular}{|&gt;{\centering\arraybackslash}m{0.5cm}|c|&gt;{\centering\arraybackslash}m{8cm}|}         \hline         \multicolumn{2}{|c|}{Classification} &amp; References \\ \hline         %\multirow{2}{*}{{\begin{turn}{90}Supervised Learning\end{turn}}}            \multirow{2}{*}{\rotatebox[origin=c]{90}{Supervised Learning}}  \end{tabular}     \caption{A Classification}     \label{tab:Machine_Learning_models} \end{table} How to sort a Google Sheets Query by a custom ordering No Surname in indian passport and given name is considered as last name in E ticket for an international flight I have booked tickets for my parents to visit Mauritius for a week and my mom's passport (given name is xxxx) doesn't have surname, so in the e-ticket form her name has been printed as "Mr xxxx". I have spoken to the travel agency and Air Mauritius, but didn't get any information regarding the issue.  Can anyone please tell me if there might be a problem boarding the flight?  I am very anxious right now since its their first international flight. How should artwork be setup for T-shirt printing? What does it mean to colour separate the artwork for T-Shirt printing? It is normally suggested to use Pantone colours for T-Shirt printing. Is it the Pantone Coated or the Pantone Uncoated? The Uncoated one has more subtle colours and we can't choose brighter shades if the design requires that. What is more appropriate for printing? Can we use gradients in T-Shirt printing or is it suggested to stick to flat colours only?   The reason for asking if gradients were ok was to use it as an option for this design:    I was considering it an option, as it will be difficult to colour separate since the textures are clip masked inside the lion. File Save dialog unreadable I just updated my iMac to Mojave, and am still trying to setup my preferences.  I tried dark mode, but did not like it (half of me apps seem to ignore it anyway).  I switched to light mode, but this too has problems. The File Save dialog shows a list of Directories and existing files, but the latter are very light grey, almost indistinguishable from the background.    I have searched the Preferences menu, but can't seem to find any setting to set normal contrast levels like in High Sierra. Show that $(p \to q) \lor (q \to p)$ is a tautology I tried to prove that $(p \to q) \lor (q \to p)$ is a tautology.  I used $p$ and $¬q$ as conditions. (Premises 1 and 5)  I managed to get to a solution, but I'm not sure if it's right.  Can you please check it?   Thank you!!!:) Creating "Inner Buffer" using ArcGIS for Desktop? I am currently searching for how to create an "Inner Buffer" in ArcGIS for Desktop?  I have a lot of polygons (houses) in one feature class, and one big polygon (in another feature class).   I want so select all houses contained in that one big polygon within a distance to the outer border (e.g. 1000 meters).  Select Layer By Location could be one possibility to solve this but I can't figure out how. Why don't gksu/gksudo or launching a graphical application with sudo work with Wayland? I installed Ubuntu 17.10. Now I am having trouble with gksu:  $ gksu -dg synaptic No ask_pass set, using default! xauth: /tmp/libgksu-HgUjgQ/.Xauthority STARTUP_ID: gksu/synaptic/8760-0-alex-XPS-15-9530_TIME4974977 cmd[0]: /usr/bin/sudo cmd[1]: -H cmd[2]: -S cmd[3]: -p cmd[4]: GNOME_SUDO_PASS cmd[5]: -u cmd[6]: root cmd[7]: -- cmd[8]: synaptic buffer: -GNOME_SUDO_PASS- brute force GNOME_SUDO_PASS ended... Yeah, we're in... Unable to init server: Could not connect: Connection refused (synaptic:8767): Gtk-WARNING **: cannot open display: :1 xauth: /tmp/libgksu-HgUjgQ/.Xauthority xauth_env: (null) dir: /tmp/libgksu-HgUjgQ   If I don't use -g, the password dialog is disabled. So looks like a problem with creating a tty for root.  Any advice? How can I find the name of a Package?