Which is greater, $e^{\pi}$ or $\pi^e$?
Comparing $\pi^e$ and $e^\pi$ without calculating them
Intuitive Bernoulli numbers Why aren't all the badges shown on the track menu? I like using the 'Track Badges' menu on my profile a lot (I know what you're going to say, I just have a knack for these things), but I keep noticing something a bit unusual.  Many of the Badges featured on the actual list do not get featured on this menu. For example, I've been hoping to be able to track progress for the Pundit badge (ten comments with score of five or more), but it doesn't show up in the menu.  Why not? What Is the Real Name of the #? fontenc changes sans serif bold font in KOMA-script Consider the following MWE:  \documentclass{article} %\usepackage[T1]{fontenc}  \begin{document}  \textbf{\textsf{Some text}}  \end{document}   The output of the above code is     and doesn't change if I uncomment the line  %\usepackage[T1]{fontenc}   Consider now the following MWE with scrartcl class instead of article:  \documentclass{scrartcl} %\usepackage[T1]{fontenc}  \begin{document}  \section{A section} \textsf{Some text} \end{document}      Uncommenting the line  %\usepackage[T1]{fontenc}   you get    As you can see, the sans serif font of the title is less  bold than without fontenc, while the normal text is not changed.  Does fontenc, combined with a KOMA-script class, load a different sans serif font, but only for bold face? Limit $\lim\limits_{x\to0}{\frac{\ln{(e+x)}-e^x}{\cos^2{x} -e^x}}$ Without using L'Hopital's rule find: $$\lim_{x\rightarrow 0}{\frac{\ln{(e+x)}-e^x}{\cos^2{x} -e^x}}$$ I found the first derivative because I planned to use Taylor series:  \begin{align} \frac{d}{dx}{\left(\frac{\ln{(e+x)}-e^x}{\cos^2{x} -e^x}\right)} &amp;=\frac{\left(\frac{1}{x+e}-e^x\right)\left(\cos^2{x} -e^x\right)-\left(\ln(x+e)-e^x\right)\left(\sin{2x}-e^x\right)} {(\cos^2{x} -e^x)^2}\\ &amp;=\frac{\frac{1}{x+e}-e^x}{\cos^2{x}-e^x}-\frac{\left(\ln(x+e)-e^x\right)\left(\sin{2x}-e^x\right)}{(\cos^2{x} -e^x)^2} \end{align}  However, it seems I haven't gone so far. Should I start from the beginning and try a different method?  Source in Croatian: 2.kolokvij, matematička analiza Word for something sad and funny at the same time What's a word for conflicting emotions that are felt at the same time? For example, loneliness, sadness, happiness, being content but also feeling as if something isn't right?  To sum up: What's a word for something that is sad and funny at the same time? Is there a case insensitive version of the  jQuery selector or should I do the work manually by looping over all elements and comparing their .text() to my string? Does a non-EU Spouse of a UK national need a visa to visit the Schengen area? I am a British national resident in the UK. My wife is Jordanian, resident in the UK with me. She has a UK biometric residency permit. We were married in the UK and the marriage is registered in the UK.   Does my wife need visas to travel with me on holiday in France and Spain? I understand from EU Directives that she does not. Would we be able to leave the UK by ferry to France if my wife does not have a French visa but can prove that she is married to me and resident in the UK? If visas are necessary but the French or Spanish consulates were NOT to grant the visas, would this be in contravention of EU Directives/Law? If the answer to question 3 is "Yes, it would be unlawful", what action can one take to get the visas? I'm trying to go into an irb session with specific environment variables from a file with this command:  $ env $(cat env.sh) irb   But when I try press Tab after I type env. to complete it, I get this following error:  $ env $(cat env.-bash: unexpected EOF while looking for matching `)' -bash: syntax error: unexpected end of file   Another interesting thing is that if I'm logged in as root, this error does not occur.   Here's the output of find ~ -uid 0:  $ find ~ -uid 0 /home/(redacted)/.rpmdb /home/(redacted)/.rpmdb/Group /home/(redacted)/.rpmdb/Conflictname /home/(redacted)/.rpmdb/Installtid /home/(redacted)/.rpmdb/Sha1header /home/(redacted)/.rpmdb/Providename /home/(redacted)/.rpmdb/__db.002 /home/(redacted)/.rpmdb/Requirename /home/(redacted)/.rpmdb/Sigmd5 /home/(redacted)/.rpmdb/__db.001 /home/(redacted)/.rpmdb/Obsoletename /home/(redacted)/.rpmdb/.dbenv.lock /home/(redacted)/.rpmdb/Name /home/(redacted)/.rpmdb/Basenames /home/(redacted)/.rpmdb/Triggername /home/(redacted)/.rpmdb/Packages /home/(redacted)/.rpmdb/Dirnames /home/(redacted)/.rpmdb/__db.003   Can anyone explain to me why this is happening and if so, how do I fix it in when I'm not a root user? Why would you not want to rollover a previous employer's 401(k) when changing jobs? Are there any valid reasons to not rollover a former 401(k) when changing jobs?  I have several little ones that I never quite got around to rolling together - with an upcoming job change, should they all be combined into my new employer's retirement plan?  If not, what else might be considered? I've recently set up the compiz cube again, and I was very happy to find that that flickering window glitch is gone! However, the cube reflection and deformation plugins are also gone.  I am running a fresh 12.10 install, and I have every compiz plugin package installed (including compiz-plugins-extra, which supposedly contains everything that compiz-fusion-plugins-extra package used to have), but those two plugins are still missing. I haven't been able to find anyone with the same problem.   Any ideas? (thanks!) Is there a term for the moment when a lot of users visit/log onto your website at the same time? Is there a term for the moment when a lot of users visit/log onto your website at the same time? Wrap Caption Around TikZ Figure In Data Extension one field 'HTML' have Data that I have shown below, Now I have to Find the 'Href', and and at the last of URL append some text like '&amp;MC='. It may have Multiple 'Href'. Please help me on this.   &lt;table width="540" style="margin: 0px; padding: 0px;" bgcolor="#ffffff" border="0" cellspacing="0" cellpadding="0"&gt;  &lt;tbody&gt;   &lt;tr&gt;    &lt;td valign="top"&gt;    &lt;h5 style="margin: 0px; padding: 0px 0px 2px; line-height: normal; font-family: &amp;quot;Segoe UI&amp;quot;, &amp;quot;Lucida Grande&amp;quot;, Verdana, Arial, Helvetica, sans-serif; font-size: 16px; font-weight: normal;"&gt;    &lt;a style="text-decoration: none;" href="https://test.4.com/testRegistration/testLobbyServlet?target=reg20.jsp&amp;eventid=897605&amp;sessionid=1&amp;key=2F3D1EB963D9DB7738BF2877DFFDBA01&amp;partnerref=Social&amp;sourcepage=register&amp;loc=zOTlocz&amp;prod=zWAz&amp;tech=zsecz&amp;prog=zOTprogz&amp;type=zOTtypez&amp;media=zWCz&amp;country=zUSz" alias="Success with Enterprise Mobility: Making email and Office 365 secure on mobile devices"&gt;    Success with Enterprise Mobility: Making email and Office 365 secure on mobile devices     &lt;/a&gt;    &lt;/h5&gt;    &lt;p style="margin: 0px; padding: 0px; line-height: 20px; font-family: &amp;quot;Segoe UI&amp;quot;, &amp;quot;Lucida Grande&amp;quot;, Verdana, Arial, Helvetica, sans-serif; font-size: 12px; font-weight: normal;"&gt;    &lt;span style="color: rgb(103, 103, 103);"&gt;    &lt;em&gt;December 9, 2014, 10:30 A.M.&amp;ndash;11:30 A.M. 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In this session featuring Brad Anderson, you will learn about the integration and the Office mobile apps while enabling secure mobile productivity.    &lt;/span&gt;    &lt;/p&gt;    &lt;/td&gt;   &lt;/tr&gt;   &lt;tr&gt;    &lt;td valign="top"&gt;&amp;nbsp;    &lt;/td&gt;   &lt;/tr&gt;   &lt;tr&gt;    &lt;td valign="top"&gt;    &lt;h5 style="margin: 0px; padding: 0px 0px 2px; line-height: normal; font-family: &amp;quot;Segoe UI&amp;quot;, &amp;quot;Lucida Grande&amp;quot;, Verdana, Arial, Helvetica, sans-serif; font-size: 16px; font-weight: normal;"&gt;    &lt;a style="text-decoration: none;" href="http://test.TTr.com/?Wt.mc_id=IG15W2NWTN&amp;loc=zOTlocz&amp;prod=zWAz&amp;prod=zWSz&amp;tech=zCLz&amp;prog=zOTprogz&amp;type=zEVz&amp;media=zOTmediaz&amp;country=zUSz" alias="Test: Everything about enterprise technology under one roof"&gt;    Test: Everything about enterprise technology under one roof    &lt;/a&gt;    &lt;/h5&gt;    &lt;p style="margin: 0px; padding: 0px; line-height: 20px; font-family: &amp;quot;Segoe UI&amp;quot;, &amp;quot;Lucida Grande&amp;quot;, Verdana, Arial, Helvetica, sans-serif; font-size: 12px; font-weight: normal;"&gt;    &lt;span style="color: rgb(103, 103, 103);"&gt;    &lt;em&gt;May 4&amp;ndash;8, 2015, Chicago, IL&lt;/em&gt;&lt;br&gt;    If you&amp;rsquo;re serious about technology, you don&amp;rsquo;t want to miss Test. This event will be the intersection of everything in enterprise technology. Get ahead in your job and your career.    &lt;/span&gt;    &lt;/p&gt;    &lt;/td&gt;   &lt;/tr&gt;  &lt;/tbody&gt; &lt;/table&gt; How can I view the contents of tar.gz file without extracting from the command-line? What are the benefits to marking a field as `readonly` in C#? What are the benefits of having a member variable declared as read only?  Is it just protecting against someone changing its value during the lifecycle of the class or does using this keyword result in any speed or efficiency improvements? How to move a file? My web application has a login page that submits authentication credentials via an AJAX call. If the user enters the correct username and password, everything is fine, but if not, the following happens:   The web server determines that although the request included a well-formed Authorization header, the credentials in the header do not successfully authenticate. The web server returns a 401 status code and includes one or more WWW-Authenticate headers listing the supported authentication types. The browser detects that the response to my call on the XMLHttpRequest object is a 401 and the response includes WWW-Authenticate headers. It then pops up an authentication dialog asking, again, for the username and password.   This is all fine up until step 3. I don't want the dialog to pop up, I want want to handle the 401 response in my AJAX callback function. (For example, by displaying an error message on the login page.) I want the user to re-enter their username and password, of course, but I want them to see my friendly, reassuring login form, not the browser's ugly, default authentication dialog.  Incidentally, I have no control over the server, so having it return a custom status code (i.e., something other than a 401) is not an option.  Is there any way I can suppress the authentication dialog? In particular, can I suppress the Authentication Required dialog in Firefox 2 or later? Is there any way to suppress the Connect to [host] dialog in IE 6 and later?    Edit Additional information from the author (Sept. 18): I should add that the real problem with the browser's authentication dialog popping up is that it give insufficient information to the user.  The user has just entered a username and password via the form on the login page, he believes he has typed them both correctly, and he has clicked the submit button or hit enter. His expectation is that he will be taken to the next page or perhaps told that he has entered his information incorrectly and should try again. However, he is instead presented with an unexpected dialog box.  The dialog makes no acknowledgment of the fact he just did enter a username and password. It does not clearly state that there was a problem and that he should try again. Instead, the dialog box presents the user with cryptic information like "The site says: '[realm]'." Where [realm] is a short realm name that only a programmer could love.  Web broswer designers take note: no one would ask how to suppress the authentication dialog if the dialog itself were simply more user-friendly. The entire reason that I am doing a login form is that our product management team rightly considers the browsers' authentication dialogs to be awful. What are the norms in Ito isometry? Itō isometry from :     Let $W : [0, T] \times \Omega \to \mathbb{R}$ denote the canonical   real-valued Wiener process defined up to time $T &gt; 0$, and let $X :  [0, T] \times \Omega \to \mathbb{R}$ be a stochastic process that is   adapted to the natural filtration $\mathcal{F}_{*}^{W}$ of the Wiener   process. Then $$      \mathbb{E} \left[ \left( \int_{0}^{T} X_{t} \, \mathrm{d} W_{t} \right)^{2} \right] = \mathbb{E} \left[ \int_{0}^{T} X_{t}^{2} \,  \mathrm{d} t \right], $$ where $\mathbb{E}$ denotes expectation with   respect to  $\gamma$. In other words, the Itō   stochastic integral, as a function, is an isometry of normed vector   spaces with respect to the norms induced by the inner products $$      ( X, Y )_{L^{2} (W)} := \mathbb{E} \left( \int_{0}^{T} X_{t} \, \mathrm{d} W_{t} \int_{0}^{T} Y_{t} \, \mathrm{d} W_{t} \right) =  \int_{\Omega} \left( \int_{0}^{T} X_{t} \, \mathrm{d} W_{t}  \int_{0}^{T} Y_{t} \, \mathrm{d} W_{t} \right) \, \mathrm{d} \gamma  (\omega) $$ and $$      ( A, B )_{L^{2} (\Omega)} := \mathbb{E} ( A B ) = \int_{\Omega} A(\omega) B(\omega) \, \mathrm{d} \gamma (\omega). $$   I was wondering what the two normed spaces are and what their norms are, so that the two normed spaces are isometric wrt their norms?  Thanks and regards! If $a,b,c \in \mathbb{R+}$ and $abc=1$ Prove That  $$S=\sum \frac{a}{a+b^4+c^4} \le 1$$  My approach:  we have $$S=\sum \frac{\frac{1}{bc}}{\frac{1}{bc}+b^4+c^4}=\sum \frac{1}{1+b^5c+bc^5}$$  Now by $AM \ge GM$ we have  $$\frac{1+b^5c+bc^5}{3} \ge b^2c^2$$ $\implies$  $$\frac{1}{1+b^5c+bc^5} \le \frac{1}{3b^2c^2}=\frac{a^2}{3}$$ Hence  $$S \le \frac{a^2+b^2+c^2}{3}$$  Can we proceed with this?