Let f be differentiable, prove that there exists $c \in (0,1)$ such that $f(c) + f'(c) = 0 $
Prove $kf(x)+f'(x)=0 $ when conditions of Rolle's theorem are satisfied .
Can't boot into Ubuntu in Windows 10 / Ubuntu dual boot Open firefox from bash file "Error: no display specified" In System Info in 11.10, the graphics driver wasn't detected. I use ACER Aspire 4750 with Intel Core i3-2340M and Intel HD Graphics 3000 graphic card  How to install the driver for my Ubuntu? Is there a way to forget node names between TikZ pictures? I have a document with several TikZ pictures in it.  I generally use simple names for the nodes such as:  \node (A) at .....  \node (B) at .....   and so forth.  Because of this I have name clashes between the various pictures.  That's generally not a problem.  However I find myself in a position where I may or may not have defined a certain node within a given picture.  So I use the following snippet to test whether the node has been defined:  \makeatletter \long\def\ifnodedefined#1#2#3{%%   \@ifundefined{pgf@sh@ns@#1}{#3}{#2}} \makeatother   Unfortunately this fails if I've already created a node by the same name in another picture.  Is there a way to scope the definitions of nodes or is there a way to undefine nodes once you no longer need them?  P.S.  I'm aware that I could embed each picture in a standalone file and import it using \includegraphics.  Unfortunately, this approach will not work for the document I'm creating.  MWE  \documentclass{article} \usepackage{tikz} \usetikzlibrary{calc}  \makeatletter \long\def\ifnodedefined#1#2#3{%%   \@ifundefined{pgf@sh@ns@#1}{#3}{#2}} \makeatother  \setlength{\parindent}{0pt} \pagestyle{empty} \begin{document}   There's no node \textbf{D} here, so I draw a triangle:\par \begin{tikzpicture}    \coordinate (A) at (0,0);   \coordinate (B) at (1,0);   \coordinate (C) at (1,1); %  \coordinate (D) at (0,1);    \ifnodedefined{D}     {  \draw (A) foreach \myn in {B,C,D} {  -- (\myn) } --cycle;  }     {  \draw (A) foreach \myn in {B,C}   {  -- (\myn) } --cycle;  }  \end{tikzpicture}     There is a node \textbf{D} here, so I draw a square:\par \begin{tikzpicture}    \coordinate (A) at (0,0);   \coordinate (B) at (1,0);   \coordinate (C) at (1,1);   \coordinate (D) at (0,1);    \ifnodedefined{D}     {  \draw (A) foreach \myn in {B,C,D} {  -- (\myn) } --cycle;  }     {  \draw (A) foreach \myn in {B,C}   {  -- (\myn) } --cycle;  }  \end{tikzpicture}      There isn't supposed to be a node \textbf{D} here.  I'm expecting a triangle, but get a square.\par \begin{tikzpicture}    \coordinate (A) at (0,0);   \coordinate (B) at (1,0);   \coordinate (C) at (1,1); %  \coordinate (D) at (0,1);    \ifnodedefined{D}     {  \draw (A) foreach \myn in {B,C,D} {  -- (\myn) } --cycle;  }     {  \draw (A) foreach \myn in {B,C}   {  -- (\myn) } --cycle;  }  \end{tikzpicture}  \end{document}   produces: Why can only some child meta sites host chat rooms? Is there any way to bypass this restriction? When I try to create a new  room from , and type "meta" in the "select a site" box, I see only 8 child meta sites. Any specific reason for this?  Update:  I just noted  (pointed out by ). The conclusion of the experiment there was:        This experiment suggests that only the meta sites, for which at least   one room already exists, are offered.   ...the distinction between beta sites and graduated sites is not sufficient to explain this.      So, if I'm reading it correctly, it is currently impossible to create a room hosted on those child metas which do not already have an existing meta room (smells like a bug!)? Or is there a way to bypass this restriction somehow?  I can think of several legitimate reasons as to why a site may choose to keep their main chat rooms and meta chat rooms separate. Killing off that freedom of choice, and that too non-uniformly, isn't a good idea. If this really is a  rather than  (for a good cause), then it should be fixed! Classifying whether a collection of objects is a set What is the REST endpoint URL to get list of site collections? If I go to SharePoint 2013 site, click on Admin -> SharePoint, you will see a list of site collections (the link is https://somename-admin.sharepoint.com/_layouts/15/online/SiteCollections.aspx)  What is the REST endpoint URL to get this list of site collections ?  I was trying _api/search/query?querytext='contentclass:sts_site' or _api/search/query?querytext='contentclass:sts_web', but it doesn't give the whole list... Highlighted source code inline with Latex/Minted? What is the difference between '/' and '//' when used for division? Is there a benefit to using one over the other? In Python 2, they both seem to return the same results:  &gt;&gt;&gt; 6/3 2 &gt;&gt;&gt; 6//3 2 Failed to start TSQL debugger I want to debug in TSQL.When I start the debug the following message box popup. In SSMS v17.2    Then I see this message:    In Microsoft Visual Studio 2015 Server Explorer same Error:    Then I see this message:    Thank You! Determine all functions satisfying $f(x + f(x + y)) + f(xy) = x + f(x + y) +yf(x)$ The below statement is a true/false exercise.  Statement: For all square matrices A and B of the same size, it is true that $(A + B)2 = A^2 + 2AB + B^2$.  My thought process: Since it is not a proof, I figure I can show by example and come to a valid conclusion based on such example.  My work:  Come up with a square matrix A and B let both be a 2 by 2 matrix(rows and cols must be same).  Matrix $A$:  $A = \begin{array}{ccc} 3 &amp; 5 \\ 4 &amp; 6 \\ \end{array} $  Matrix $B$:  $B =  \begin{array}{ccc} 5 &amp; 8 \\ 9 &amp; 4 \\ \end{array} $  $A + B =  \begin{array}{ccc} 8 &amp; 13 \\ 13 &amp; 10 \\ \end{array}$  $(A + B)^2 =  \begin{array}{ccc} 233 &amp; 234 \\ 234 &amp; 264 \\ \end{array}$  $A^2 =  \begin{array}{ccc} 29 &amp; 45 \\ 36 &amp; 56 \\ \end{array}$  $(AB) =  \begin{array}{ccc} 60 &amp; 44 \\ 74 &amp; 56 \\ \end{array}$  $2(AB) =  \begin{array}{ccc} 120 &amp; 88 \\ 234 &amp; 112 \\ \end{array}$  $B^2 =  \begin{array}{ccc} 97 &amp; 72 \\ 81 &amp; 88 \\ \end{array}$  $A^2 + 2AB + B^2 =  \begin{array}{ccc} 246 &amp; 205 \\ 265 &amp; 256 \\ \end{array}$  Based my above work, the answer is false.   Is there another way to approach the problem? It seems like a lot of work needed to be done for a true/false question which raised my suspicion about whether there is a better way to look at the problem. How to remove Ubuntu from dual boot system with Windows? I wish to remove Ubuntu and I'm not quite sure how. I know it has something to do with partitions. I have 3 partitions. 1. OS [683 GB]  2. Recovery [14 GB] 3. Ubuntu 12.04 LTS (E:)  I know it says Ubuntu but when I installed Ubuntu I think I put 14 gigabytes for it so I think its the recovery one but I'm not sure. I could have sworn I put more than 700 megabytes for it.  I have googled this and I can't seem to find an answer. Any help would be nice. Install Java JDK and JRE on Debian 8 I installed Debian 8, I would like to install Java JRE and JDK. I use  and it works.  But, I am afraid because it's a script hosted in a repository. I would like to understand why it doesn't work when I put the extract of  in /usr/java/jre1.8.0_73 directory as . I added the path variable with PATH=/usr/local/jdk1.8.0/bin:$PATH export PATH as explained in  but it doesn't work.  Even if I try to install OpenJDK, the package isn't found. I don't understand why it's so complicated to install Java on Debian; it is very simple on Ubuntu. I would like someone give me step-by-step instructions to install it. Err 80 appears when I turn on my Canon EOS 5D Mark II Recently when on holiday in Italy my 5DII stopped powering up. Turn the switch on and - nada. Pulling the battery and popping it back in brings the camera to life, however as soon as the camera goes in to sleep mode, or I turn the power off, the problem returns. Sometimes the camera shows Error 80 at this point:     Err 80      Shooting is not possible due to an error.    Turn the camera off and on again or re-install the battery.   I've seen various posts on the interwebs about pulling the clock battery and leaving the camera for a while - have tried this and also replaced the clock battery to no avail.   Has anyone else had this problem - did the body have to go back to Canon for repair or did you manage to fix it? clerics have the ability  (PHB, p. 62):     When a creature within 5 feet of you that you can see hits you with an attack, you can use your reaction to cause the creature to make a Dexterity saving throw. The creature takes 2d8 lightning or thunder damage (your choice) on a failed saving throw, and half as much damage on a successful one.   It doesn't specify what the DC of the saving throw is.   I assume it uses the spell save DC, even though it technically isn't a spell?     Spell save DC = 8 + your proficiency bonus + your Wisdom modifier What is the opposite of "personification"? I want a word that means the opposite of personification.  What is the correct word for describing people with the characteristics of an object/as if they are objects?  I found the word chremamorphism on some forums, but it doesn't seem to be included in the two online dictionaries I searched. Any idea what kind of tool should I but to fix the loose left crank on my bike? I found this  but not sure if it's gonna suit. Or is it enough to buy only nut driver? In $ \triangle ABC$ show that $ 1 \lt \cos A + \cos B + \cos C \le \frac 32$ Am I allowed to make a Stack Overflow clone? SO is not Open-Source, but I like the whole idea of Stack Overflow :   Giving bounties for Questions Up/Downvoting Questions The Badges The intelligent use of Ajax-Technologies Highly Rated users have administrative powers Reputation system Editing posts like a wiki   So I would like to program a (what is it called) Q&amp;A site / board / wiki system. Am I allowed to?