Prove that $$\log(t):=\lim_{n\to\infty}n(t^{1/n}-1),$$ for any $t&gt;0$.
How do I show that $\ln(x) = \lim_{n\to\infty} n (x^{1/n} - 1)$?  I ran into this identity on . I haven't been able to find any proof online and my efforts to get from $\ln(x) := \int_1^x \frac{\mathrm dt}t$ to that limit have been a failure.
How do you setup a TeX document to self publish a book online? I am a casual TeX user. Mostly I have used it to type up some reports/homeworks for class in my graduate engineering work. In the past I have used document type "article". And then kept all the defaults.  I need to self publish something online. At the highest level I would like to know: How do you setup a TeX document to self publish a book online?  Some more low level questions:   Is there a document type for "book" and what is its name? I am looking at Amazon Createspace. : filetype=pdf, trim size, margins (gutter and outside margins). All of these various trim size, margins gutter/outside can be adjusted in the Tex document?   Has anyone seen any good TeX templates for Amazon Createspace? If you could demonstrate how to tweak a specific "book" document type that would be very helpful also.    Other than the above questions, please feel free to offer any other sort of help since I am completely new to this process (advice, links to good tutorials, links to wikibooks). Join table depending on value of column in main table Get different and common items in two arrays with LINQ Prove that: area of triangle $S_{ABC}=p \cdot R$, where p is half perimeter of triangle $DEF$ Prove that: area of triangle $S_{ABC}=p \cdot R$, where p is half perimeter of triangle $DEF$. $AD,CF, BE$ are altitudes. Is there a simple way? Enable HTTP DELETE requests on Apache server I need to configure my server to permit the http delete method.  currently, I get the following error when I attempt to make this call:    HTTP/1.1 405 Method Not Allowed Date: Mon, 11 Apr 2011 20:56:23 GMT Server: Apache/2.2.17 (Win32) PHP/5.3.5 Allow: GET,HEAD,POST,OPTIONS,TRACE Content-Length: 233 Keep-Alive: timeout=5, max=98 Connection: Keep-Alive Content-Type: text/html; charset=iso-8859-1     I have searched far and wide and have not been able to come up with an answer as to how I can configure the server to allow this request.  Someone please help as it has put a stop to my project. Erf as term for plot of land in a town or city. Is this word only used in southern Africa? The Free Dictionary website states and so does Wikipedia:     erf [ɜːf]   n pl erven [ˈɜːvən]   (Engineering / Civil Engineering) South African a plot of land, usually urban, marked off for building purposes   [Afrikaans]   The term erf is used in legal documentation and technical English throughout South Africa and Namibia, maybe even further afield in the region.  Is it used anywhere else, except maybe the Dutch/Flemish regions in Europe, where I assume the term originated?  An example:      The client purchased Erf 132, Windhoek for a large sum of money. He intends to build a house on this erf.   The capitalisation of "Erf 132" is commonplace, since it is a definition of a location. This is similar to capitalisation of towns or cities. I find it slightly awkward, but that is how it is done. I would like to change a file extension from *.txt to *.text. I tried using the basename command, but I'm having trouble on changing more than one file.  Here's my code:  files=`ls -1 *.txt`  for x in $files do     mv $x "`basename $files .txt`.text" done   I'm getting this error:  basename: too many arguments Try basename --help' for more information How to prove a cross is not locally homeomorphic to an euclidean space? Consider the subset $X = \{(x, 0) \mid -1 \lt x \lt 1\} \cup \{(0, y) \mid -1 \lt y \lt 1\} \subset \Bbb R^2$. It's just two open segments intersecting at $(0, 0)$.  How do you show that $X$, equipped with the subspace topology of $(\Bbb R^2, \lvert \lvert \cdot \rvert \rvert_2)$, is not locally homeomorphic to an euclidean space because of the point $(0, 0)$ ? How to start a new Linux distro? How come such different methods result in the same number, $e$? Does a non-trivial solution exist for $f'(x)=f(f(x))$? Stack Exchange doesn't allow me to answer protected questions because I gave away earned rep in bounties Update 2014-04-17 04:47 UTC: Stable, with some odds and ends to clean up      The main MSO/MSE sites are stable, but there are plenty of corners left to sweep. For details, see:    Not all of them mind you, just Meta Stack Overflow into Meta Stack Exchange.  I'll have you know, factually, that we really did believe this would take place in six-to-eight weeks when it was , but we've finally got a tentative date established.  If things go according to plan, we'll begin the operation shortly after 8:30 PM EDT on the 16th, completing everything within a few hour window. Ideally, all service disrupting endeavors will be completed within the first hour, which include:   The availability of Meta Stack Overflow The availability of Stack Overflow (more on this shortly) The availability of Chat on Meta Stack Overflow   As you know, we'll be bolting on a standard issue per-site meta on Stack Overflow, while breaking the link between what will have become Meta Stack Exchange and Stack Overflow. There's some irritable innards in that particular region, so we'll be asking folks to expect the unexpected during the maintenance window. Affected sites will be in and out of read-only mode, or quite possibly just down for maintenance while we're doing the actual break.  I'll be posting a system message on both Meta Stack Overflow as well as Stack Overflow itself 24 hours before we begin the actual work.   Did I say tentative in a six-to-eight-something time frame again? Why yes, I did - we're currently running some tests on the dev tier to simulate the split as closely as possible, so that we can better anticipate quirks that we need to address prior to actually doing it.  Once the sites have actually been stood up functionally on the production tier, we're going to get to work on finishing touches. This will include things like site settings (which determine bits of text you see in the question prompts, rep thresholds, etc) and all sorts of other fine tuning.  Once we're done:   Stack Overflow will have a blank, empty child meta site just like every other site The new Meta Stack Exchange will be up and running All rooms on Chat Meta Stack Overflow will be moved to Chat Meta Stack Exchange  I'll send over about 150 - 200 questions from MSE to MSO, most of which will be tag or SO-specific feature related posts that got buried by the network stuff without resolution.   If the tentative date moves, I'll update this post with the new date. However, we do not anticipate this happening any later than Saturday, April 19 - in the case that we see down time we can't mitigate and need to do it on a weekend.  The ground work is basically done, we're finishing up sanity now with a great deal of confidence, and we're pretty certain that we'll hit between those dates, if not directly on the tentative 16th.  Questions? Kvetch? Anonymous confessions? Answer below, and I'll address each in comments. Problem with TP-Link TL-WN823N Recently I installed Ubuntu 16.04 but cant get the usb wifi adapter to work properly , can anyone help me?  When wifi adpater is plugged , the lsusb output:  Bus 001 Device 003: ID 2357:0109 Bus 001 Device 002: ID 0e0f:000b VMware, Inc.  Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub  Bus 002 Device 004: ID 0e0f:0008 VMware, Inc.  Bus 002 Device 003: ID 0e0f:0002 VMware, Inc. Virtual USB Hub Bus 002 Device 002: ID 0e0f:0003 VMware, Inc. Virtual Mouse Bus 002 Device 001: ID 1d6b:0001 Linux Foundation 1.1 root hub   When wifi adapter is unplugged , the lsusb output:  Bus 001 Device 002: ID 0e0f:000b VMware, Inc.  Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub Bus 002 Device 004: ID 0e0f:0008 VMware, Inc.  Bus 002 Device 003: ID 0e0f:0002 VMware, Inc. Virtual USB Hub Bus 002 Device 002: ID 0e0f:0003 VMware, Inc. Virtual Mouse Bus 002 Device 001: ID 1d6b:0001 Linux Foundation 1.1 root hub country code TLD vs second level ccTLD I'm really worried about professionalism.  My site would be something like http://mywebsite.uy instead of http://mywebsite.com.uy.  What do you think about this practice? What should I have in mind at the moment of choosing one? In my device (iPhone 6, iOS v8.0.2, app v1.2.0.138) whenever I receive a notification and I tap it in order to open the application, the screen that is displayed is blank.  I need to quit the app, re-open it, go to my 'inbox' and tap the last notification in order to see the question screen, focused on the comment.  This is not new (for me) in v1.2.0.138; it has been happening for at least the last ~7 updates that I've done. Accidently deleted /usr/lib, how do I restore it? HTML text input allow only numeric input Is there a quick way to set an HTML text input (&lt;input type=text /&gt;) to only allow numeric keystrokes (plus '.')? Total number paths between two nodes in a complete graph There is a type and search drodown which will appear after user type in the value. I need to click on the dropdown which contains the name of the drop down field.   The problem here is that there is no unique attribute present (No unique class, no unique name) &amp; the id keeps on changing after every login so cannot take id also.