Differentiating Exponential Functional Equation
A function $f: \mathbb R \to \mathbb R$ satisfies equation $f(x+y)=f(x)f(y)$ for all $x,y\in \mathbb R $
English version of Ubuntu with Italian keyboard I want to install Ubuntu in ENGLISH (UK) but I have an ITALIAN keyboard, which has a different layout to the English keyboard. How can I install Ubuntu in English but select an Italian layout for the keyboard. I tried, but it would only allow me to select an English keyboard. Thanks How old is SpongeBob? I don't mean how old is the series, I mean what is SpongeBob's age if he were a real person. I ask because his age seems to be ambiguous in the show.   He has a full-time job He has his own house He is always referred to as a kid (especially in the movie) He acts childish and immature In one episode, he was pretending to be an adult/grown-up Any questions relating to status updates, or asking if anything is going to be patched for these vulnerabilities should be closed as duplicates of this question.    are in the news right now and sound pretty severe. I don't see any security updates from Ubuntu that cover these vulnerabilities.  What is Ubuntu doing about these vulnerabilities, and what should Ubuntu users be doing?  These are CVE-2017-5753, CVE-2017-5715 and CVE-2017-5754. How do I change permissions on a FAT32 formatted drive? I am using Microsoft Visual C++ on Windows and Qt Creator on Ubuntu. I can't change permissions on my flash drive (FAT32), even as root.  How can I change permissions on a FAT32 flash-drive? Why does the experience-to-next-level not change between some levels? At every level from 1st to 11th, the experience needed to reach the next level (from the current level) increases every level. However, this pattern gets broken for most of the later levels:   Going from 10th to 11th takes 21,000xp (= 85k - 64k), but 11th to 12th takes only 15,000xp! (= 100k - 85k). Both 13th and 14th level only take extra 20k experience each, i.e. the amount needed doesn't increase between those two levels. Levels 16 and 17 similarly only need 30k experience each, and 18 and 19 only need 40k experience each.   Why does the last half of the experience chart have some of these levels maintain the same experience costs, and even briefly decrease the experience cost for 12th level? What is the bit size of long on 64-bit Windows? Not to long ago, someone told me that long are not 64 bits on 64 bit machines and I should always use int. This did not make sense to me. I have seen docs (such as the one on Apple's official site) say that long are indeed 64 bits when compiling for a 64-bit CPU. I looked up what it was on 64-bit Windows and found         Windows: long and int remain 32-bit in length, and special new data types   are defined for 64-bit integers.      (from )  What should I use? Should I define something like uw, sw ((un)signed width) as a long if not on Windows, and otherwise do a check on the target CPU bitsize? Measure the size of a PostgreSQL table row I have a PostgreSQL table. select * is very slow whereas select id is nice and quick. I think it may be that the size of the row is very large and it's taking a while to transport, or it may be some other factor. I need all of the fields (or nearly all of them), so selecting just a subset isn't a quick fix. Selecting the fields that I want is still slow. Here's my table schema minus the names: integer                  | not null default nextval('core_page_id_seq'::regclass) character varying(255)   | not null character varying(64)    | not null text                     | default '{}'::text character varying(255)   |  integer                  | not null default 0 text                     | default '{}'::text text                     |  timestamp with time zone |  integer                  |  timestamp with time zone |  integer                  |   The size of the text field may be any size. But still, no more than a few kilobytes in the worst case. Questions  Is there anything about this that screams 'crazy inefficient'? Is there a way to measure page size at the Postgres command-line to help me debug this? I'm trying to install the drivers to my wireless adapter ():   I have already tried the following:  sudo add-apt-repository ppa:hanipouspilot/rtlwifi sudo apt update sudo apt install rtl8192eu-dkms   But I'm getting the following error:  E: Unable to locate package rtl8192eu-dkms   I have also tried manually downloading and installing it, but I'm getting this:  make make ARCH=x86_64 CROSS_COMPILE= -C /lib/modules/4.6.0-kali1-amd64/build M=/root/Desktop/20140812_rtl8192EU_linux_v4.3.1.1_11320  modules make[1]: *** /lib/modules/4.6.0-kali1-amd64/build: No such file or directory.  Stop. Makefile:1323: recipe for target 'modules' failed make: *** [modules] Error 2   edit: lsusb output  root@kali:~# lsusb Bus 002 Device 002: ID 8087:0024 Intel Corp. Integrated Rate Matching Hub Bus 002 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub Bus 001 Device 004: ID 8087:07da Intel Corp.  Bus 001 Device 003: ID 1bcf:2c0e Sunplus Innovation Technology Inc.  Bus 001 Device 002: ID 8087:0024 Intel Corp. Integrated Rate Matching Hub Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub Bus 004 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub **Bus 003 Device 002: ID 2357:0107**   Bus 003 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub Word for someone that always has to be right Is there a word for someone that always has to be right? The person gets angry if they are not. Computing $\int_{0}^{\pi}\ln\left(1-2a\cos x+a^2\right) \, dx$ For $a\ge 0$ let's define $$I(a)=\int_{0}^{\pi}\ln\left(1-2a\cos x+a^2\right)dx.$$ Find explicit formula for $I(a)$.   My attempt: Let  $$\begin{align*} f_n(x) &amp;= \frac{\ln\left(1-2 \left(a+\frac{1}{n}\right)\cos x+\left(a+\frac{1}{n}\right)^2\right)-\ln\left(1-2a\cos x+a^2\right)}{\frac{1}{n}}\\ &amp;=\frac{\ln\left(\displaystyle\frac{1-2 \left(a+\frac{1}{n}\right)\cos x+\left(a+\frac{1}{n}\right)^2}{1-2a\cos x+a^2}\right)}{\frac{1}{n}}\\ &amp;=\frac{\ln\left(1+\dfrac{1}{n}\left(\displaystyle\frac{2a-2\cos x+\frac{1}{n}}{1-2a\cos x+a^2}\right)\right)}{\frac{1}{n}}. \end{align*}$$ Now it is easy to see that $f_n(x) \to \frac{2a-2\cos x}{1-2a\cos x+a^2}$ as $n \to \infty$. $|f_n(x)|\le \frac{2a+2}{(1-a)^2}$ RHS is integrable so $\lim_{n\to\infty}\int_0^\pi f_n(x)dx = \int_0^\pi \frac{2a-2\cos x}{1-2a\cos x+a^2} dx=I'(a)$. But  $$\int_0^\pi \frac{2a-2\cos x}{1-2a\cos x+a^2}=\int_0^\pi\left(1-\frac{(1-a)^2}{1-2a\cos x+a^2}\right)dx.$$ Consider $$\int_0^\pi\frac{dx}{1-2a\cos x+a^2}=\int_0^\infty\frac{\frac{dy}{1+t^2}}{1-2a\frac{1-t^2}{1+t^2}+a^2}=\int_0^\infty\frac{dt}{1+t^2-2a(1-t^2)+a^2(1+t^2)}=\int_0^\infty\frac{dt}{(1-a)^2+\left((1+a)t\right)^2}\stackrel{(*)}{=}\frac{1}{(1-a)^2}\int_0^\infty\frac{dt}{1+\left(\frac{1+a}{1-a}t\right)^2}=\frac{1}{(1-a)(1+a)}\int_0^\infty\frac{du}{1+u^2}=\frac{1}{(1-a)(1+a)}\frac{\pi}{2}.$$ So $$I'(a)=\frac{\pi}{2}\left(2-\frac{1-a}{1+a}\right)\Rightarrow I(a)=\frac{\pi}{2}\left(3a-2\ln\left(a+1\right)\right).$$  It looks too easy, is there any crucial lack?  $(*)$ — we have to check $a=1$ here by hand and actually consider $[0,1), (1,\infty)$ but result on these two intervals may differ only by constant - it may be important but in my opinion not crucial for this proof. I am running 12.04 LTS. It's a pretty default installation and is the only OS on this machine.  I have two users one has administrator rights the other does not. I accidentally removed administrator rights from the "admin" user.  I tried to  but that requires reaching GRUB during boot but I cannot get there because my /etc/default/grub has GRUB_HIDDEN_TIMEOUT=0 and changing that to a positive integer requires admin privileges to save the changes and run sudo update-grub.  Should I boot from LiveCD? The  discouraged my a bit. Right now all I have handy is an install DVD from 11.10, but that did not help me much.  Not sure what to do now.  Any suggestions?  NOTE: 12.04 does not have an admin group and I have not enabled root Is it possible to "upgrade" from a 32bit to a 64bit installation? As per title, I wish to know if I can, after a successful 32bit setup and consequent software installations, update to a 64bit version.  I know how to partition (actually one of the solutions is to set /, /etc, /home, /var/www, and /opt as separate partitions) and I know that a clean install is way better than a dirty one, yet I would like to know if/how it's possible to do that. Prepositions used with "inquire" Okay. If I wanted to redirect the output of a program to a file, I'd do something like this  prog &gt; file   If I wanted to redirect both stdout and stderr to that file, then I'd do  prog &gt; file 2&gt;&amp;1   This is all well and good if you want the output to go to the file. But what if you want the output to go to the file and yet still go to stdout/stderr? So, the output is saved in the file, but you can still see it on the console as the program is running. Is there a way to do that? And if so, how? Performing reverse clip in ArcMap? Is there a way to perform a 'reverse' of the clip function in ArcMap?  I am not exactly sure how to explain this so here is a diagram: I am trying to work through Hartshorne's book and while working through one of the exercises, I need to show the following:  Let $k$ be an algebraically closed field. Let $Y \subseteq A^3$ be the set $Y=\{(t,t^2,t^3)\;|\;t \in k\}$. Show that $Y$ is an affine variety.  The rest of the problem I have completed. I'm just not sure how to show that this set is closed and irreducible. I assume that they intend for $A^3$ to have the Zariski topology. Classify all groups with order $pq$, $p$ is not equal to $q$ I am reading the following material:  . At page 5, there is a proof classifying all groups with order $pq$(they are all primes and $p$ is not equal to $q$). I am lost in the last two sentence, which claims the semidirect product are all isomorphic. Could someone help me to understand it? Thanks! Is there a sorted collection type in .NET? I'm looking for a container that keeps all its items in order.  I looked at SortedList, but that requires a separate key, and does not allow duplicate keys.  I could also just use an unsorted container and explicitly sort it after each insert.  Usage:   Occasional insert Frequent traversal in order Ideally not working with keys separate from the actual object, using a compare function to sort. Stable sorting for equivalent objects is desired, but not required.  Random access is not required.   I realize I can just build myself a balanced tree structure, I was just wondering if the framework already contains such a beast. The standard titlepage is quite simple. I am looking for a very  and need help customizing my title page.  It should match the  classicthesis doctoral thesis template  Below a minimal working example:   \documentclass[12pt,a4paper,footinclude=true,twoside,headinclude=true]{scrbook} \XeTeXinputencoding iso-8859-1 \usepackage[marginparsep=8pt,left=3.5cm,right=3.5cm,top=3cm,bottom=3cm]{geometry}  \usepackage[parts,pdfspacing,dottedtoc]{classicthesis}    \frontmatter  \begin{document}     \pagestyle{scrheadings}        %this is the place to set up my cover sheet.       %*******************************************************      % Abstract     %*******************************************************    %\renewcommand{\abstractname}{Abstract}    \pdfbookmark[1]{Résumé}{Résumé}   \begingroup    \let\clearpage\relax    \let\cleardoublepage\relax    \let\cleardoublepage\relax       \chapter{Résumé}     Résumé de la thèse en français\dots      \vfill      \chapter*{Summary}   Résumé de la thèse en anglais\dots    \endgroup             \vfill     \end{document} Why don't I get $e$ when I solve $\lim_{n\to \infty}(1 + \frac{1}{n})^n$?