Is the L'Hopital's rule true when using limits on $\mathbb{C}$ (the complex field)?  I don't know if it is only valid using the real numbers $\mathbb{R}$... is that the case?
I have a question about something I'm wondering about. I've read somewhere that L'Hopitals rule can also be applied to complex functions, when they are analytic. So if have for instance:  $$ \lim_{z \rightarrow 0} \frac{\log(1+z)}{z} \stackrel{?}{=} \lim_{z \rightarrow 0} \frac{1}{(1+z)} = 1 $$  Now i'm wondering if this is correct? Also if we take $|z|&lt;1$, is it then correct?  Thanks,
Poisson Distribution of sum of two random independent variables $X$, $Y$ $X \sim \mathcal{P}( \lambda) $ and $Y \sim \mathcal{P}( \mu)$ meaning that $X$ and $Y$ are Poisson distributions. What is the probability distribution law of $X + Y$. I know it is $X+Y \sim \mathcal{P}( \lambda + \mu)$ but I don't understand how to derive it. On some icons I am seeing a two blue arrows at the top the right pointing towards each other. I first noticed it on the icons on folders which I archived which happened randomly. I archived the folder and the text went blue as expected, then when I went to the folder again the text was black and the folder icon has these arrows. When I just recently installed Office 2007, I noticed the same arrows on the icons for the programs. OS: Windows 10 Pro 64-bit (the latest update: 1115) Application: Microsoft Office 2007 suite and file explorer Does the Force wane as you age? @Valorum said     ...not to mention the sheer strain that comes from continually using the Force at an advanced age.   To my feeble mind, this doesn't make sense. Approaching 900 years old, Yoda is still as strong as any whippersnapper in terms of Force power and usage. Despite his old age, Obi Wan shouldn't have any problems with using his Force powers.  This got me to thinking, does the Force begin to leave you as you age? Is it a flow of Force power that goes down based on (I hate to say this) a decrease in midichlorian count as you approach your expiration date? How to configure Ubuntu as an LDAP client? How to configure Ubuntu 12.04 as LDAP client with PAM modules? wpf combobox binding Use LaTeX to simulate old typewriter written texts This question led to a new package:      I'm giving my students an old exam and barely remembered to change the date at the top. A colleague and I joked about how long we could reuse the same exam, and it made me wonder if I could use LaTeX to create an exam that looked like it was written in 1963 on a typewriter.  Here's what I'd like to see:   Typewriter font even in math mode. (Several ways to accomplish this; is there a "best" way?) Slight inconsistencies in the printing of each letter. I attempt this below adapting code taken from . Each word has a random vertical shift, though I'd like to see it reduced to each letter having its own vertical shift. Other typewriter-like irregularities would be great. It would be great if math-mode delimeters \left(, \right}, etc., can be created in a piece-meal fashion as they did in days of old. Fraction bars, tops of square-root symbols -- any horizontal line, really -- is made up of a series of en-dashes that don't quite match up.   Here is what I've come up with so far:  \documentclass[10pt]{article}% This is a document class providing more font size options \usepackage{graphicx} \usepackage{ifthen} \usepackage[textwidth=7.5in,textheight=9.5in]{geometry} \pagestyle{empty}  % thanks to Bruno Le Floch: https://tex.stackexchange.com/q/9331/4012 % and in his comments to https://tex.stackexchange.com/a/29458/4012 \usepackage[first=-1,last=1]{lcg}% you can play around with these values \makeatletter \newcommand{\globalrand}{\rand\global\cr@nd\cr@nd} \makeatother  \newcommand{\randomvshift}[1]{\globalrand\raisebox{\value{rand}pt}{#1}}  %%% thanks to Martin Scharrer: https://tex.stackexchange.com/q/11598/4012 \makeatletter \def\typewriter#1{%     \@typewriter#1 \@empty } \def\@typewriter#1 #2{%    \randomvshift{#1}\space    \ifx #2\@empty\else     \expandafter\@typewriter    \fi    #2% } \makeatother \begin{document}\tt  \typewriter{Math 101 Fall 1963}  \begin{enumerate} \item   \typewriter{$\frac{\texttt{d}}{\texttt{dx}}\texttt{(x)}^2$}  \item \typewriter{State the Fundamental Theorem of Calculus.}  \end{enumerate}  \end{document} iPhone Apps in Waiting mode for the last 4 days I tried to download the "Dictionary Free" app from the App Store four days ago, but it's been stuck in "Waiting" ever since. I've tried everything: rebooting the phone, restoring from an iTunes backup, side-loading the app from iTunes, but nothing has worked.  When I turn Airplane Mode on and then off again, I get an alert popup that says "Unable to download application. It will be available for download when you log in to the iTunes Store on your computer".  I've tried what it recommends, but nothing seems to work. Can I smoothly upgrade from one LTS to next LTS release? How do I add a Pokestop to my area? How do I add a Pokestop to an area that has none? It is an area where there are tons of businesses but unless I drive about a mile from my work area there are no Pokestops.   I want to add one since we have 1000's of people in the work area, a lot of them play Pokemon Go, and we all can't leave work to drive a mile away to get to a Pokestop area.   Plus it would be nice to be able to capture Pokemon on our breaks. Is there a way to combine custom settings with custom labels ? So that the output from a setting value would be a custom label ?   To explain:  In example, we have an international organisation, and say countries are stored as an ISO code. As this is a limited and stable set of data, using custom settings would be the appropriate way to deal with say the full country name.   The issue arises when I do not just want to store the English country name, but want to have it translatable, presenting the right translation depending on the user's locale. Now, this is the point where I'd like to integrate custom settings with custom labels.  So that say the custom setting with name 'some iso code' doesn't return the full country name, but Label.Country'some iso code', which is than automatically translated in the right version.   Sounds good right. But as custom settings are fixed to certain types, as far as I've gotten is put the label name in the settings as a string value. And then .. i'm stuck :).  No way to cast a string to a Custom label, or have it be interpreted (and translated) as such, or is there ?   I'm aware this can be done in a custom object &amp; apex, I was hoping for a more automated, "cleaner", less resource consuming way, better integrated, configurable way.  Additional clarrification: *The goal is to extend the use of custom labels (translation workbench), by adding a mapping from any data-based value to a custom label.*   While we could do a long matching process in apex, it would be faster &amp; neater if the custom settings mechanism could be used. There are disadvantaged to custom objects, they require soql &amp; apex, while custom settings &amp; custom labels are cached. They too can be used in many other places. Countries were an example, I'd use this mechanism for every variable value that needs to be translatable. Normally while searching using grep, the command I was using was this:  grep -nri "String"   whereas most of my colleagues do this:  grep -nri "String" *   What does the latter do (the * part)? How can you reduce ambient noise from servers? Different ways to prove there are infinitely many primes? How to subtract days from a plain Date? How can I check the SMART status of a SSD or HDD on current versions of Ubuntu 14.04 through 20.04? How can I check the SMART status of a drive under 14.04 and beyond? I've seen  but it doesn't seem to apply under 14.04 and later. We encountered a Vampire Spawn in the 10-foot-high basement of an old church. The first strike was mine, after which the creature attacked my ally and retreated onto the ceiling as the thundering roar of my Booming Blade punished its retreat. Still inexperienced and unsure about my reach, after a short consultation with my mind, I decided to spend my turn switching to my trusty crossbow and make some distance.  However this turned out to be a mistake, since right after, the creature was in in my face trying to gouge out my eyes. Due to my nimbleness I managed to avoid its attacks. Regretting my earlier choice to change weapons I was left with the options to switch weapons and miss another turn, attack with disadvantage, or use my crossbow as an improvised melee weapon and trust in Booming Blade to hold the enemy in place after I disengaged.  Perhaps I should have switched weapons, but I decided that 1d4 (improvised weapon) + 1 (magic ring) + 1d8 (booming blade) was good enough. I missed.  On the plus side, it was my crossbow's sneak attack assisted bolt that finally slayed the Vampire by piercing its heart.    In this situation, would it have been possible to just attack upwards instead of changing to the crossbow?  In session, this was something to be looked up later and decided against, but I haven't found any rules on attacking in 3D.  With me being more than 5 feet in height and my melee attack range considered to be 5 feet, I should have been able to reach the ceiling itself, not to mention the Vampire Spawn hanging from it.    As for exact measurements (read this part only if you enjoy pointlessly over-analyzing things):  My character is 5 feet 6 inches/5.5 feet, which gives an  (for a human, my character is a Kenku), . This should give me a height of 8.3 to 8.9 feet from standing statically.    Testing it in real life, my estimated and standing reach match to less than 0.2 inches of the estimation on the site and I'm just shy of reaching my ceiling standing statically. As a test I tried moving as if I was attacking my ceiling and based on where I could feel my hand touch the ceiling, the length of my fingers and how much distance I lacked to reach my ceiling, I estimate about 0.4 feet in additional height. Considering that I'm taller than my character, let's say that gives 0.3 feet, increasing the height to 8.6 - 9.2 feet and that's still without changing how you hold the handle of the sword. In addition, just lying on the ground, my torso and legs measure about 0.6 feet.  Because my Kenku isn't a human, only a humanoid, it's impossible to estimate arm length which influences standing reach, however, considering that birds usually have a high wingspan and long legs, I think it's reasonable to assume that the arms should be as long, if not longer than, a human's.    So that would require the Vampire Spawn to be flat against the ceiling without any parts hanging down more than 0.2 to 0.8 feet for it to be outside of my reach. I consider that unlikely.  What are the actual rules for this type of scenario, or how do you handle it in your group? Should I be allowed to melee attack an enemy that's on a ceiling or low in the air? gain admin access to sql express 2008 I am struggling to understand zero inflated distributions. What are they? What's the point?  If I have data with many zeroes, then I could fit a logistic regression first calculate the probability of zeroes, and then I could remove all the zeroes, and then fit a regular regression using my choice of distribution (poisson e.g.).  Then somebody told me "hey, use a zero inflated distribution", but looking it up, it does not seem to do anything differently than what I suggested above? It has a regular parameter $\mu$, and then another parameter $p$ to model the probability of zero? It just does both things at the same time no? How do I restore .bashrc to its default? I've been trying to install Android developer tools on Eclipse, and I followed the information in .  Like the video said, I added the following two lines of code to the .bashrc file:  export PATH=$(PATH):-/android-sdk/tools/ export PATH=$(PATH):-/android-sdk/platform-tools/   It seems, however, that this did not help me to install the Android files on Eclipse, as I am still having problems with that. What's more, it seems that I can't make any command in the terminal without getting a major error now! Every time I try to make a command in the terminal I get the following message:     The command could not be located because '/usr/bin' is not included in   the PATH environment variable.   Is there away to restore .bashrc to its default? How do I make multiple spawn points in minecraft vanilla?