Proving the limit of $\left(\frac n{n+1}\right)^n$is $e^{-1}$
Finding the limit of $\left(\frac{n}{n+1}\right)^n$
Refactoring RadioGroup setter code? I have a Toshiba Satellite laptop. My charger has stopped working.  I have access to a Lenovo charger. Can I use this charger on my laptop? VS10 debugger error: Test host process exited unexpectedly If I run history, I can see my latest executed commands.  But if I do tail -f $HISTFILE or tail -f ~/.bash_history, they do not get listed.  Does the file get locked, is there a temporary location or something similar? Finding $\int^{\infty}_{0}\frac{\ln^2(x)}{(1-x^2)^2} dx$ Calculate  $$\int^{\infty}_{0}\frac{\ln^2(x)}{(1-x^2)^2}dx$$   I have tried to put $\displaystyle x=\frac{1}{t}$ and $\displaystyle dx=-\frac{1}{t^2}dt$  $$ \int^{\infty}_{0}\frac{t^2\ln^2(t)}{(t^2-1)^2}dt$$  $$\frac{1}{2}\int^{\infty}_{0}t\ln^2(t)\frac{2t}{(t^2-1)^2}dt$$  $$ \frac{1}{2}\bigg[-t\ln^2(t)\frac{1}{t^2-1}+\int^{\infty}_{0}\frac{\ln^2(t)}{t^2-1}+2\int^{\infty}_{0}\frac{\ln(t)}{t^2-1}dt\bigg]$$  How can I solve it? How fast does gravity propagate? I am trying to show that $X^n-Y^m$ is irreducible in $\Bbb{C}[X,Y]$ iff $\gcd(n,m)=1$ where $n,m$ are positive integers.    I showed that if $\gcd(n,m)$ is not $1$, then $X^n-Y^m$ is reducible. How to show the other direction. Please help. How to make a spiked sphere? I know how to make it manually with cone rotation around the sphere. but maybe there's much simpler solution or addon that has that option, preferably not very high poly solution.  Also if possible I would like the spikes not to be very pointy if that makes any sense      Thanks How many times has the matter in our solar system been recycled from previous stars? I've got a basic understanding of these facts:   The Universe is a little over 13 billion years old.  Our galaxy is almost that old. Our solar system is roughly 4.6 billion years old. The heavier elements (Carbon, oxygen, etc...) are only produced by stars.   When our solar system coalesced, the matter that makes up the planets came from a previous generation of stars.  (Meanwhile our Sun is busy making its own slightly-heavier elements, but those aren't ours.  Those belong to the next "generation" after our star dies.)  So we're all sitting on a rock whose matter was spewed out of a star (or stars) that preceded this solar system. But what I want to know is:  How many cycles of coalescing, fusing, nucleosynthesis, exploding -- and then repeating the cycle -- have this atoms in this ball of rock I'm standing on been through?    How do you know this?  Can you tell by the make-up of the matter in the solar system?  Looking around the Orion arm to see remnants of our former home? I'm using Ubuntu GNOME 16.10 and was trying to install WPS Office. I tried to install using software centre But it wasn't installing without giving any error logs. Then I opened it with Gdebi installer. Here is what I saw.    I have already trying enabling multiverse repositories.  Edit: I have downloaded the amd64 package from the WPS official site, but even now installing through terminal I still get the missing dependencies error. I am using the 2D Animation preset and so far every new scene I made had the same bright white background. Now my two latest scenes (created with 'copy settings') have a light grey background even though they are set to white. There's also no difference in surface, nodes or strength.  There are apparently exist different background shades with an off-white color but selecting the white one doesn't help either How can I create a coffee cream effect with Photoshop? Today I would like to create a coffee cup with the cream floral on it as a text by using Photoshop. It looks like you order a cup of hot cappuccino and the bartender will draw a flower with cream on the surface of coffee but now I want to make it like a text to present a tittle.     I just need to do the cream text effect, no need to draw the whole cup of coffee since i can't use some images. So anyone can tell me how to do this cream effect on Photoshop.  Thanks in advance for any feedback! What is the most CPU efficient way to ensure that NumLock is on? Situation: I have a script watching over NumLock status, well not really watching, but turning it On every 1 second. The script is running in the background.  Reasoning: I often accidentally turn off NumLock. And I have no indicator of NumLock status on the keyboard.  OS, DE, DM, WM, xmodmap:  :  $ lsb_release -a  No LSB modules are available. Distributor ID: LinuxMint Description:    Linux Mint 18 Sarah Release:    18 Codename:   sarah   :  echo $DESKTOP_SESSION  cinnamon   :  cat /etc/X11/default-display-manager  /usr/sbin/mdm   :  wmctrl -m | head -n 1  Name: Mutter (Muffin)   :  xmodmap -pm  xmodmap:  up to 4 keys per modifier, (keycodes in parentheses):  shift       Shift_L (0x32),  Shift_R (0x3e) lock        Caps_Lock (0x42) control     Control_L (0x25),  Control_R (0x69) mod1        Alt_L (0x40),  Alt_R (0x6c),  Meta_L (0xcd) mod2        Num_Lock (0x4d) mod3       mod4        Super_L (0x85),  Super_R (0x86),  Super_L (0xce),  Hyper_L (0xcf) mod5        ISO_Level3_Shift (0x5c),  Mode_switch (0xcb)   My original Bash script follows:  #!/bin/bash  while true do    numlockx on    sleep 1s  done   As you can see, the script does not care about current status of NumLock. It just keeps turning it on.  Goal: I would like to make the script at least somewhat CPU efficient.  Question: What is the most CPU efficient way to ensure that NumLock is On in Linux (Mint 18)? I am afraid that listing doesn't support javascript.  \begin{lstlisting}[language=javascript] ... \end{lstlisting}   What am I doing wrong? I was caught cheating on an exam, how can I minimize the damage? I got caught cheating in a two-hour engineering exam consisting of 100 multiple choice questions which was done online through the  e-learning software. I feel like my life is almost over.  Having not studied well and having no time to study, I decided to cheat. I know there are no excuses for cheating. Before the exam I dug up research about moodle exams, and it turned out you can take the exam anywhere you want to as long as you have the quiz password. Taking advantage of this, I went up to my engineering library and asked a close friend who was taking the exam to send me the quiz password before he starts.  What I had prepared:   Calculator (was not allowed during the quiz). Printed material (consisted of more than 200 pages). Google search engine (on a laptop ready to help). Whatsapp (to ask questions for a friend who took the quiz last year).   As I sat down, I did the first 50 questions, suddenly the quiz froze and moodle told me:      you are not allowed to take the exam from this location.   While I was leaving, one instructor responsible for the course (there are 5) came and found me. She accused me of cheating, took my mobile and made come with her to a huge office where two instructors searched all my mobile (took the name of my friend who gave me the password), and started talking to me, asking for all details of this crime. They took and confiscated my phone and looked at everything: Whatsapp conversations, all my emails, and images. The instructor took the mobile from my hand without asking me and kept it with her. It seems that the instructors are going to report me as well as my friend who sent me the password for the exam.  The university's Student Code Conduct said that cheating will result in one of the following: a Dean's Warning, Suspension, or Expulsion. If any of that happens, my future is over. A dean's warning will cancel my financial aid. A suspension would be for at least two years, and coming back would require a lot of work. An expulsion will be definite.  I've learned the lesson about cheating, now how can I fix this? How can I prevent the five instructors from reporting me? It's obvious that I should speak to them, but what should I say? What can I do? My future is almost over, but many of you are teachers and instructors here, what can I do to fix this?    EDIT: Wow, it has been almost 3 years. I would like to update on how I dealt with the situation.   Lesson: It was obvious to never ever cheat under any circumstances, and it was not whether you'd get caught or not.    Consequences: I received a Dean's warning but the financial aid wasn't revoked. However, I couldn't stay in the department as engineering was not for me and I was even ashamed to stay in the university.  What happened next: I transferred to an ABET-accredited Computer Science institution and I graduated with distinction in 2.5 years. It was extremely stressful as I had taken 6 major courses (18 credits) in one semester, but I had to do it.  Future plans: I'm going for an MSc in Computer Science in St Andrews next year. I've recently searched how I could get the application's directory in Java. I've finally found the answer but I've needed surprisingly long because searching for such a generic term isn't easy. I think it would be a good idea to compile a list of how to achieve this in multiple languages.  Feel free to up/downvote if you (don't) like the idea and please contribute if you like it.  Clarification:  There's a fine distinction between the directory that contains the executable file and the current working directory (given by pwd under Unix). I was originally interested in the former but feel free to post methods for determining the latter as well (clarifying which one you mean). How does one prove that every finite group is isomorphic to a subgroup of an alternating group? Does tourist visa (90 days) apply after a long-term visa ends in Schengen countries? Why was the alien threat in The Next Generation episode "Conspiracy" never followed up? In the Star Trek The Next Generation episode  Picard and crew are drawn into an alien conspiracy to take over the Federation. This ends with Picard and Riker destroying an alien "mother" beast, but not before it manages to send a signal to an uncharted sector of space. The feeling at the end of the episode is that this will be a threat that the intrepid crew of the Enterprise would be facing again at some point, but this never happens.   Why was the implied threat at the end of this episode never brought up again on the show? How does the T-1000 see? In Terminator 2: Judgement Day, how does the T-1000 sense things? It's made of mimetic poly alloy; however, does it have a retinal scan camera like the T-X or T-800, or is just molecules that allow it to see what it does? In other words: let's say it is made out of nanobots. Would a group of these nanobots provide the capability of sight? Kind of like humans with cells that  make up the brain? I have always wondered whether James Cameron explained this on a special edition or if the topic was left up for insight from Terminator fans. From what I get from the whole mimetic poly alloy and some of the extra scenes, it seems to feel its way out to get information. Of course, it's very much not blind! Thoughts?