$(1+x/n)^{1/n}$ monotone increasing?
Show that $\left(1+\frac xk\right)^k$ is monotonically increasing
Moving all files to a new computer, my concern is links Why is there a big delay after entering a wrong password? What is the relationship between size of object with distance? How does the size/length of an object vary with distance?   Is it a logarithmic relationship? exponential? linear?   I plotted a curve of the size/length of an object for different distances from the camera, and the curve looked exponential/logarithmic. I was trying to understand the reasoning behind that. Promote tag wiki creation for new tags I want to determine whether a multi-line string ends with a line containing specified pattern.  These code failed, it doesn't match.  s=`echo hello &amp;&amp; echo world &amp;&amp; echo OK` [[ "$s" =~ 'OK$' ]] &amp;&amp; echo match Can a coin with an unknown bias be treated as fair? When I launch certain programs from the command line like eclipse and document viewer in 11.10 it spews a load of information that seems inconsequential.   Also when they are run in the background they sometimes continue to produce output to the terminal which I am currently working on, which is irritating.  I would like them just launch and keep the background stuff in the background. My reasoning is that if you launch these programs through the GUI (eg double clicking on an icon) these messages are never shown to me, so I don't need them in the command line. I'm wondering how can I simulate a sample of n Weibull distribution lifetimes that include Type I right-censored observations. For instance lets have the n = 3, shape = 3, scale = 1 and the censoring rate = .15, and the censoring time = .88.  I know how to generate a Weibull sample but I do not know how to generate a censored data that have type I right-censored in R.  T = rweibull(3, shape=.5, scale=1) Usage of "as if" as interjection My question concerns the usage of "as if" as an idiomatic interjection. The references I have consulted (etymonline, online dictionaries, etc.) seem to agree that "as if" is used in this context to convey incredulity or doubt. This is how I have always thought of it.  The other day, I was with friends who used "as if" to express their surprise and joy about a wedding proposal. They weren't being sarcastic or incredulous; they were genuinely happy about the proposal. Here is a loosely paraphrased version of what they said:  "As if they're getting married!"  Is my friends' usage of "as if" standard? Is it a primarily regional distinction? (I am in Ontario, Canada right now.) The closest example we could come up with is someone says "I can't believe that you won first prize!" Of course, the person can and does believe it, so their words ought not to be taken literally. Is it the same idea with "as if"? Calculate $\sum_{k=1}^n (-1)^{k+1} \binom{n}{k}\frac{1}{k}$ I searched wide and far and couldn't come up with a title for a movie I watched somewhere around the mid-90ies up to early 00's as a rerun in late-night television (in Germany, specifically on Vox; but I'm sure it was an American movie to begin with).  Basically, what I remember from the story revolves around a crew in a space station or maybe space ship of some sort. Some crew members murder other crew members and there is some kind of door they are not supposed/unable to go through. Late in the movie they do go through the door and I'm pretty sure one of the first views is a skeleton of a dead security guard. It turns out the whole thing was some kind of simulation gone wrong and they find themselves to be in a (nuclear?) wasteland. And that's pretty much the revelation/wrap-up of the movie, as I recall it.  I would be delighted if somebody had any idea what movie this could be :) Thanks!  EDIT: The whole movie was in color and I think it was feature-length, not just 45 mins. what is the surface area of a cap on a hypersphere? According to , let the sphere have radius $R$, then the surface area a spherical cap of height $h$ and base radius $a$ is given by $$S=2\pi Rh=2\pi(a^2+h^2).$$  What is this value for an n-dimensional hypersphere? If it helps simplify the problem we can assume $R=1$ and $a=0.5$.   Many thanks. As far as I know, it's possible to create a radially polarised ring magnet, where one pole is on the inside, and the field lines cross the circumference at right angles.    So imagine if I made one which was shaped like a sector of a torus.    Then I forced a load of these magnets into a complete torus.     Clearly this magnet is impossible because there's no way for the field lines to get back into the middle. So what happens to the field in this case? Does it disappear completely? Do the magnets blow up? How to download packages from a command-line given repository? What should be the default title case for non-technical questions? As an example, this question is titled using sentence case. I've been going to lots of different meta sites (especially this one), and I think the needle bent on my oh-me-oh-my-my-ocd-oh-meter.  Can we please standardize on using either:   Sentence case Title Case AP Style Title Case   ... and then we can look at just converting titles automatically? This would be a switch, of course, but I'd only imagine turning it off on sites where program code or symbols might be present in titles. Or, it could just become part of editing guidelines.    Additionally, is this a horrible idea?   To see the differences between them, you can put any arbitrary title into  (we have no affiliation with them, it's just a tool I sometimes recommend to people).  We would also eventually adopt this for static routes, but I'm mostly talking about questions. Periodic function implies periodic primitive? If $f$ is a periodic function with $T = \pi$, does that mean that $F$ (a primitive of $f$) has the same period ? What about the inverse implication (periodic primitive implies periodic function) ? Interactive / Real time code compilation for stackoverflow.com. That will improve the answer correctness of the stackoverflow.com.  When adding a new code block, let the user try to compile the code and see the result. It will be useful to demonstrate class designs, algorithms, and logics. Isn't less just more? When I do more filename and less filename, it would seem that the resulting terminals are quite similar. I can navigate and search through my files identically (j, Space, /pattern, etc.).  I find it hard to believe that less is more and vice versa. Are there any differences between the two? CPU governor changes automatically to "performance" under load I have a Lenovo T570 with Xubuntu 18.04 LTS. My current issue is that my cpu speed stepping is kind of going nuts and does what ever it thinks its best.  Sample: when I run my IDE and cpu load increases during build time, the governor changes automatically. I caught the moment during compiling my project with the following call:  martin@martin-ThinkPad-T570:~$ while cat /sys/devices/system/cpu/cpu0/cpufreq/scaling_governor; do sleep 1; done powersave powersave performance performance   cpufreq-info tells me this:  martin@martin-ThinkPad-T570:~$ cpufreq-info  cpufrequtils 008: cpufreq-info (C) Dominik Brodowski 2004-2009 Report errors and bugs to cpufreq@vger.kernel.org, please. analyzing CPU 0:   driver: intel_pstate   CPUs which run at the same hardware frequency: 0   CPUs which need to have their frequency coordinated by software: 0   maximum transition latency: 4294.55 ms.   hardware limits: 400 MHz - 3.50 GHz   available cpufreq governors: performance, powersave   current policy: frequency should be within 3.50 GHz and 3.50 GHz.                   The governor "performance" may decide which speed to use                   within this range.   current CPU frequency is 3.25 GHz. analyzing CPU 1:   driver: intel_pstate   CPUs which run at the same hardware frequency: 1   CPUs which need to have their frequency coordinated by software: 1   maximum transition latency: 4294.55 ms.   hardware limits: 400 MHz - 3.50 GHz   available cpufreq governors: performance, powersave   current policy: frequency should be within 3.50 GHz and 3.50 GHz.                   The governor "performance" may decide which speed to use                   within this range.   current CPU frequency is 3.36 GHz. analyzing CPU 2:   driver: intel_pstate   CPUs which run at the same hardware frequency: 2   CPUs which need to have their frequency coordinated by software: 2   maximum transition latency: 4294.55 ms.   hardware limits: 400 MHz - 3.50 GHz   available cpufreq governors: performance, powersave   current policy: frequency should be within 3.50 GHz and 3.50 GHz.                   The governor "performance" may decide which speed to use                   within this range.   current CPU frequency is 3.26 GHz. analyzing CPU 3:   driver: intel_pstate   CPUs which run at the same hardware frequency: 3   CPUs which need to have their frequency coordinated by software: 3   maximum transition latency: 4294.55 ms.   hardware limits: 400 MHz - 3.50 GHz   available cpufreq governors: performance, powersave   current policy: frequency should be within 3.50 GHz and 3.50 GHz.                   The governor "performance" may decide which speed to use                   within this range.   current CPU frequency is 3.36 GHz.   Please take a look at     current policy: frequency should be within 3.50 GHz and 3.50 GHz.       The governor "performance" may decide which speed to use   Afterwards to go back to powersave I use my little script:  martin@martin-ThinkPad-T570:~$ cat cpu_freq_save.sh  #!/bin/bash sudo cpufreq-set -g powersave -c 0 --min 400MHz sudo cpufreq-set -g powersave -c 1 --min 400MHz sudo cpufreq-set -g powersave -c 2 --min 400MHz sudo cpufreq-set -g powersave -c 3 --min 400MHz   Which resets the min frequency and the governor but as soon as I compile again with my IDE every time the governor and the min frequency changes again.  Any idea how I can disable that automatic change?  PS: If you need more details, just tell me where to find them and I will provide them How to inject keystrokes via a shell script? I'm trying to inject keystrokes into the input daemon so as to simulate typing from a Bash script. Is this possible, and if so, how can I make it happen?