Find: $\displaystyle \lim_{x\to -\infty} \dfrac{\ln (1+e^x)}{x}$ (no L'Hospital)   I'm getting a hard time solving this limit. The book shows 1 as the answer, Wolfram Alpha shows 0.   I could solve easily another problem when the denominator was $e^x$ but got stuck on this one.   No L'Hospital rule can be used.  Hints and full answers are appreciated. Sorry if this is a duplicate.
Show that $$\lim_{x \to \infty} \frac{\log(1 + e^x)}{x} = 1$$ How do I prove this? Or how do we get this result? Here $\log$ is the natural logarithm.
Node Package Manager got corrupted in some way, now it cannot be installed I ran into a problem today when I decided to use npm update -g in a nodejs app directory. This was a bad decision, because it caused me to run into a .   The solution is to reinstall nodejs and npm. Unfortunately when I go to install npm using sudo apt-get install npm it doesn't work.  The full error in the terminal is here:  Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that  some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation: The following packages have unmet dependencies:  npm : Depends: nodejs but it is not going to be installed    Depends: node-abbrev (&gt;= 1.0.4) but it is not going to be installed    Depends: node-ansi but it is not going to be installed    Depends: node-archy but it is not going to be installed    Depends: node-block-stream but it is not going to be installed    Depends: node-fstream (&gt;= 0.1.22) but it is not going to be installed    Depends: node-fstream-ignore but it is not going to be installed    Depends: node-github-url-from-git but it is not going to be installed    Depends: node-glob (&gt;= 3.1.21) but it is not going to be installed    Depends: node-graceful-fs (&gt;= 2.0.0) but it is not going to be installed    Depends: node-inherits but it is not going to be installed    Depends: node-ini (&gt;= 1.1.0) but it is not going to be installed    Depends: node-lockfile but it is not going to be installed    Depends: node-lru-cache (&gt;= 2.3.0) but it is not going to be installed    Depends: node-minimatch (&gt;= 0.2.11) but it is not going to be installed    Depends: node-mkdirp (&gt;= 0.3.3) but it is not going to be installed    Depends: node-gyp (&gt;= 0.10.9) but it is not going to be installed    Depends: node-nopt (&gt;= 2.1.1) but it is not going to be installed    Depends: node-npmlog but it is not going to be installed    Depends: node-once but it is not going to be installed    Depends: node-osenv but it is not going to be installed    Depends: node-read but it is not going to be installed    Depends: node-read-package-json (&gt;= 1.1.0) but it is not going to be installed    Depends: node-request (&gt;= 2.25.0) but it is not going to be installed    Depends: node-retry but it is not going to be installed    Depends: node-rimraf (&gt;= 2.2.2) but it is not going to be installed    Depends: node-semver (&gt;= 2.1.0) but it is not going to be installed    Depends: node-sha but it is not going to be installed    Depends: node-slide but it is not going to be installed    Depends: node-tar (&gt;= 0.1.18) but it is not going to be installed    Depends: node-which but it is not going to be installed E: Unable to correct problems, you have held broken packages.   What can I do to get npm properly installed and running again?  Thanks. Method for batch layout of images into PDF sheets I have 100,000 identically-sized, but unique, PNG/JPG images which I want to automatically layout onto A4 sheets which can then be exported as print-ready PDFs.  So assuming I can fit 8 of these images per page in a 4x2 grid, I'm looking to input my 100,000 images and output 12,500 PDFs.  I'm a programmer so I could probably write a script to do this myself (e.g. PHP/Python), but I was wondering whether there are any tools/scripts/software that already exists that can do this automatically. Why won't attribute modifiers add up on my armor? Deriving the speed of the propagation of a change in the Electromagnetic Field from Maxwell's Equations I've been told that, from Maxwell's equations, one can find that the propagation of change in the Electromagnetic Field travels at a speed $\frac{1}{\sqrt{\mu_0 \epsilon_0}}$ (the values of which can be empirically found, and, when plugged into the expression, yield the empirically found speed of light)  I'm really not sure how I would go about finding $v = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$ simply from Maxwell's equations in the following form, in SI units --  $$\nabla \cdot \mathbf{E} = \frac {\rho} {\epsilon_0}$$  $$\nabla \cdot \mathbf{B} = 0$$  $$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}$$  $$\nabla \times \mathbf{B} = \mu_0 \left( \mathbf{J} + \epsilon_0 \frac{\partial \mathbf{E}} {\partial t} \right)$$  Is what I believe true? (that the speed of propagation is derivable from Maxwell's Equations)  If not, what else is needed?  If so, can you provide a clear and cogent derivation? Rename ToC, List of Figures, References I would like to know how to rename the standard list of figures, table of contents, and references. What I saw so far relying on \renewcommand{\contentsname}{name} did not work so far.  Here's the list of preambles I use:  \documentclass[12pt]{report} \usepackage[utf8]{inputenc}  \usepackage{fourier} \pagestyle{headings} \usepackage{marvosym} \usepackage[pdftex]{graphicx} \usepackage[margin=2.5cm]{geometry} \usepackage{rotating} \usepackage{amsmath} \usepackage{booktabs} \usepackage{url} \usepackage{natbib} \usepackage{setspace} \linespread{1.5} \newenvironment{remark}{\par\mbox{}\par\noindent{\bfseries             \emph{Remark}\/}:\normalfont}{\par} \newenvironment{defin}{\par\mbox{}\par\noindent\bfseries \emph{\Pointinghand\     }\normalfont}{\par} \setcounter{toc**strong text**depth}{2}  \usepackage[colorlinks=true, a4paper=true, pdfstartview=FitV, linkcolor=blue, citecolor=blue, urlcolor=blue]{hyperref} \pdfcompresslevel=9 \setstretch{1.0} %vertical stretch \usepackage{fontspec} \setmainfont[BoldFont       = AvenirNextRoundedPro-Bold.otf , ItalicFont     =AvenirNextRoundedPro-Italic.otf]{AvenirNextRoundedPro-Reg.otf} \defaultfontfeatures{Mapping=tex-text} \usepackage{multirow} \usepackage{array} \usepackage{booktabs} \usepackage{hyperref} \hypersetup{ hidelinks, } \usepackage{ragged2e} \usepackage{euler} \usepackage[euler-digits,euler-hat-accent]{eulervm} \usepackage[labelfont=bf]{caption} \usepackage{wrapfig} \usepackage{amsmath} \usepackage{amssymb}  \usepackage[english]{babel} \usepackage[nottoc]{tocbibind} %Adds "References" to toc \usepackage{titlesec} \titleformat{\chapter}[display]{\bfseries\huge}{\filleft\Large\chaptertitlename~\thechapter}{1ex}{\vspace{1ex}\filright}[\vspace{0.5ex}\titlerule] \usepackage{float} \usepackage{etoolbox} \makeatletter \patchcmd{\@caption}{\csname the#1\endcsname}{\csname fnum@#1\endcsname:}{}{} \renewcommand*\l@figure{\@dottedtocline{1}{2em}{6em}} \let\l@table\l@figure  \makeatother % default for 3rd arg: 2.3em - for list of figures and tables \usepackage{background} \definecolor{textcolor}{HTML}{000000}             \newcommand\Text{c\quad o\quad n\quad f\quad i\quad d\quad e\quad n\quad t\quad i\quad a\quad l} \SetBgColor{textcolor}\SetBgOpacity{0.3}\SetBgAngle{90}         \SetBgPosition{current page.center} \SetBgVshift{-0.33\textwidth} \SetBgScale{1.8}         \SetBgContents{\sffamily\Text} %for confidential   I also use TexMaker. I do not know how relevant it is, but here my document language is set to English (even if it's not the language I write in, in that document, but it isn't a problem seemingly). What I also saw is that, if I remove babel and the references, I can rename my ToC and LoF, LoT. But I need the references though. Any tip would be very welcome!  Edit: I cannot provide text data from my project, because it is confidential. Here's what I can provide from the main document. Here is what I can include more.  \begin{document} \include{02_front}  \setcounter{page}{0} \pagenumbering{roman} \tableofcontents \listoffigures \listoftables \newpage \setcounter{page}{0} \pagenumbering{arabic} \chapter{blabla} \section{test é è åøæ î} \appendix \bibliographystyle{plain}  \bibliography{80_refs}   \end{document}   Also, I actually finished writing my thesis but I need to summarize it briefly in another language, am would be extremely unwilling to test and remove packages that "might be" not very useful. I literally only have to change these names of ToC, LoF, ToF and references. I found that every character has a "Personal Item" in his inventory after you start the game. My question is: What is the purpose of it? I mean yeah you could sell it for 100$ but that really is absolutely nothing. It also doesn't have any stats so what can I use it for? What does "may they rot there" mean? POSTFIX main.cf permission denied find exclude directory Preventing robots from crawling specific part of a page As a webmaster in charge of a tiny site that has a forum, I regularly receive complains from users that both the internal search engine and that external searches (like when using Google) are totally polluted by my users' signatures (they're using long signatures and that's part of the forum's experience because signatures makes a lot of sense in my forum).  So basically I'm seeing two options as of now:   Rendering the signature as a picture and when a user click on the "signature picture" it gets taken to a page that contains the real signature (with the links in the signature etc.) and that page is set as being non-crawlable by search engine spiders).  This would consume some bandwidth and need some work (because I'd need an HTML renderer producing the picture etc.) but obviously it would solve the issue (there are tiny gotchas in that the signature wouldn't respect the font/color scheme of the users but my users are very creative with their signatures anyway, using custom fonts/colors/size etc. so it's not that much of an issue). Marking every part of the webpage that contains a signature as being non-crawlable.   However I'm not sure about the later: is this something that can be done?  Can you just mark specific parts of a webpage as being non-crawlable? Can't save my render as an image I seem to be having issues when I try and save the output file as a .png, or .jpeg for that matter. I've set up my user preferences, File, Render Output to my desktop as well as render output in the editor window. What am I missing here? I'm obviously very new to this program and your help would be appreciated. Thanks for your time Best way to strip punctuation from a string It seems like there should be a simpler way than:  import string s = "string. With. Punctuation?" # Sample string  out = s.translate(string.maketrans("",""), string.punctuation)   Is there? TL;DR: how does an Ubuntu flavor iso installation ( for example Lubuntu ) differ from installing a desktop package via apt-get ? (for instance sudo apt-get install lubuntu-desktop)  Context for the question:   Some time ago I answered a question on AskUbuntu , where I tested in virtual machine removing unity-desktop and installing ubuntu-gnome-desktop. That makes the boot logo ( plymouth ) change, desktop changes, different packages get installed (gnome-network-manager instead of network-manager , if I am not mistaken). It appeared that in effect I've switched to different Ubuntu flavor, even though I started out with the standard Ubuntu system. Hence the question: what differentiates the pre-made Ubuntu flavor iso from installing a package ? Is it all the same base underneath the hood or does installation from iso have specific configurations ? If it's possible to install a flavor via package manager, why then separate flavor iso's exist ? (obvious answer is user convenience, but I think there has to exist other reasons. Canonical is a business , and it makes not a lot of sense for a business to provide additional flavor iso , if a sysadmin or end-user can get the same thing via package manager by themselves). I would like to know if there are any other tenses or grammatical structures to use for speaking about the future apart from will (perfect tense included), going to, simple and continuous present.  I mean not the obvious ones. For example, simple present (I could never have imagined it could be used for the future).     My mom arrives tomorrow.   I go to the doctor at 4 o'clock this afternoon. What order do triggered abilities happen in if multiple things trigger at the same time? I had several humans on the battlefield.  On turn three, I played . On turn four, I played . On turn five, during my upkeep, this question came up.  At this point, I need to draw/reveal three cards. If I reveal a human, Descendants' Path will allow me to cast it without paying its mana cost.  So, does it matter when I draw the human?  The static abilities state "at the beginning up your upkeep..." which leads me to believe that those two draws/reveals would happen before my normal draw. If that's the case, does the draw order happen in the same order that I played the enchantments?  In the end, that's how we decided to do it. I drew first for Triumph of Ferocity, then I revealed for Descendants' Path, then I drew for my turn. Did we do it right? I thought people would be working on little code projects together, but I don't see them, so here's an easy one:  Code that validates a valid US Zip Code. I know there are ZIP code databases out there, but there are still uses, like web pages, quick validation, and also the fact that zip codes keep getting issued, so you might want to use weak validation.  I wrote a little bit about zip codes in a side project on my wiki/blog:    There is also a new, weird type of zip code.     I can do the javascript code, but it would be interesting to see how many languages we can get here. Proving convergence of sums: If $\sum_{n=1}^{\infty}a^2_n$ and $\sum_{n=1}^{\infty}b^2_n$ converge then $\sum_{n=1}^{\infty}a_nb_n$ converges Evaluation of $ \sum_{k=0}^n \cos k\theta $ I just wanted to evaluate  $$ \sum_{k=0}^n \cos k\theta $$  and I know that it should give  $$  \cos\left(\frac{n\theta}{2}\right)\frac{\sin\left(\frac{(n+1)\theta}{2}\right)}{\sin(\theta / 2)}   $$  I tried to start by writing the sum as  $$ 1 + \cos\theta + \cos 2\theta + \cdots  + \cos n\theta $$  and expand each cosine by its series representation. But this soon looked not very helpful so I need some clue about how this partial sum is calculated more efficiently ... Are wormholes really a valid shortcut to distant points in the universe? Lately I encountered a few times references to wormholes as a way to reach distant places in the universe in a short time. I have to admit I don't have a proper knowledge of the mathematics behind wormholes (although I won't mind a complete GR explanation in the answer, if necessary). All I know is that wormholes are usually compared to something analogous to a tunnel through the planet Earth to reach distant places in less time. The problem is, if I want to reach the other side of the planet I have to travel 20.000 km on its surface and "only" 12.000 km through its center. While the latter is surely shorter, it's still more than 50% of the initial value and this is the best-case scenario. For shorter distances, the difference becomes more and more negligible.  Now, I know enough of GR to understand that this explanation could be a simplification so extreme that any comparison makes little to no sense, but I'm curious to understand if the same problems arise for wormholes too. I don't really care if wormholes exist, are traversable by spaceships and both the crew and the vessel can survive the travel undamaged, I know they are still a theoretical construct and probably there is more than one formulation for it. What I'm really interested in is:   How much shorter will the travel be? I'm interested in Earth proper time, because if the reduction is only in the spaceship proper time, the we can achieve the same result "simply" by traveling closer to the speed of light. Does the amount of reduction in time depend on the distance between the endpoints? If so, it seems unpractical to travel to near stars through wormholes, if the spacetime geometry of our galaxy doesn't help somehow (local curvature should be higher than global curvature). How to get client date and time in ASP.NET?