Without Cauchy Integral Formula or Residues: $\int_{L}\frac{dz}{z^{2}+1}$
Proof using Cauchy Integral Theorem
I am currently running Ubuntu 11.10 off of a SanDisk 16GB USB. I installed it using a Live USB with the following partition configuration:  6GB Primary /dos   FAT32 5GB Logical /      ext4 5GB Logical /home  ext4   I don't have a hard disk, and don't see myself getting one anytime soon.   I rely solely on this 16GB, and two other 4GB USBs, one of which I used as the LiveUSB. I bring the USBs around, and even use the install at work.   I previously used an install that used a swap file. It functioned fine for the most part, save for a few slow moments, but I came across , and it got me thinking about my USB's life, so I reinstalled with the current config.   My problem now is that it is slower. Applications like Firefox would hang more often. In my previous setup (the automatically partitioned setup), Firefox would start hanging if I was running an unzip or install task on the same partition as /.   Now however, it would hang if I had another window open i.e. the system settings window. My guess is that it may have something to do with the swap file or the install being on a Logical partition rather than a Primary partition, but I don't know.   Any insight as to why it has slowed down? Remove suggested apps option in iOS 10 As far as I can tell, suggested apps show themselves based on location.  There are two places where these suggested apps show themselves to me:   At the bottom left of the multitask screen when I double press the home button At the bottom left of the lock screen    article describes how to get rid of the small app icon appearing in the bottom left. However, this method is for iOS 8, and I am now on iOS 10, where I am unable to find iTunes and App Store > Suggested Apps.   How can I get rid of these (in my opinion) annoying little things? Why is a (simple) mask not recommended for asymptomatic COVID-19 patients? Information about (simple) mask wearing (concerning covid19) is a complete mystery to me. On several official places it is not recommended for a person without symptoms to wear a mask. For example:    (time 0:20)  or here:    However no explanation is given - which makes me wonder (and even angry). I think everybody should wear a mask because:   Many persons feel ashamed wearing it, even those with symptoms. If everybody wears it, they do not feel ashamed and wear it. As far as I know, one is (wrt covid19) contagious before developing symptoms. So if everybody wears the mask also these people do.   The two above points act as a collective protection.   Simple mask certainly will lower "getting / spreading illness" probability. Of course the "holes" (in a simple mask) are too big to prevent completely virus to enter (or get out when coughing), but it lowers probability! Even if it lowers the transmission probability by e.g. 5%, it might be a lot. As a hypothetical example: it might reduce R0 from 1.02 to 0.97 and so stop the virus spread so fast.   The videos are full of self-contradiction. In the same video    time 0:50 the lady says I should wear a mask if I am in contact with an infected person... why if it is inefficient?  Question: What are reasons for not recommending wearing a mask? Can I charge a computer through its USB port? After reading a couple of answers and comments on some SQL questions here, and also hearing that a friend of mine works at a place which has a policy which bans them, I'm wondering if there's anything wrong with using backticks around field names in MySQL.  That is:  SELECT `id`, `name`, `anotherfield` ... -- vs -- SELECT id, name, anotherfield ... Since the last update (v1.0.85), I am getting all the question pages blank on the Android app. For those who are confused with the image, I'm using RtL (Right-to-Left) layout.        If I scroll down (quite a bit) I can see the question. But even then I cannot see the question title, the related comments or answers.         App Version: 1.0.85 Device Manufacturer: LGE Device Model: LG-D620   OS Version: 5.0.2 (152541901f156) Question: If $(1+x)^n=\binom{n}{0}+\binom{n}{1}x+\binom{n}{2}x^2+\dotsm+\binom{n}{n}x^n$, prove that $\binom{n}{1}-2\binom{n}{2}+3\binom{n}{3}-\dotsm+(-1)^{n-1}n\binom{n}{n}=0$  My attempt:  I wrote the expression for $\binom{n}{k}$ for each term in the L.H.S and then tried to simplify but could not reach the R.H.S.  Please help. I have no idea on how to begin. I am not allowed to use calculus. Converting HTML to plain text in PHP for e-mail iPhone App CrashReport Why is $x^0 = 1$ except when $x = 0$? Laravel - Populating Select List with Derived Values I have the following file:  ---------- 1 Steve Steve 341 2017-12-21 01:51 myFile.txt   I switched the user to root in the terminal, and I have noticed the following behaviors:   I can read this file and write to it. I can't execute this file. If I set the x bit in the user permissions (---x------) or the group permissions (------x---) or the others permissions (---------x) of the file, then I would be able to execute this file.   Can anyone explain to me or point me to a tutorial that explains all of the rules that apply when the root user is dealing with files and directories? I use HD Tune to measure performance of the hard drive.  The tests typically take 2-3 minutes and the transfer rate of a regular hard drive decreases dramatically as the test comes to a close.    However, the SSD drive performance stays the same over (pic below) the life of the test.  This happens on all my computers.  Why is that? How to mount a RAM disk on startup? I'm trying to mount a RAM disk on startup with this:  /Users/Aram/Development/Tools/ramdisk.sh  diskutil erasevolume HFS+ "RamDisk" `hdiutil attach -nomount ram://800000`   com.aram.ramdisk.plist  &lt;?xml version="1.0" encoding="UTF-8"?&gt; &lt;!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN"          "http://www.apple.com/DTDs/PropertyList-1.0.dtd"&gt; &lt;plist version="1.0"&gt;     &lt;dict&gt;         &lt;key&gt;Label&lt;/key&gt;         &lt;string&gt;com.aram.ramdisk&lt;/string&gt;         &lt;key&gt;ProgramArguments&lt;/key&gt;         &lt;array&gt;             &lt;string&gt;/bin/sh&lt;/string&gt;             &lt;string&gt;/Users/Aram/Development/Tools/ramdisk.sh&lt;/string&gt;         &lt;/array&gt;         &lt;key&gt;RunAtLoad&lt;/key&gt;         &lt;true/&gt;     &lt;/dict&gt; &lt;/plist&gt;   And then running:   sudo chown root:wheel /Library/LaunchDaemons/com.aram.ramdisk.plist sudo launchctl load -w /Library/LaunchDaemons/com.aram.ramdisk.plist   But I get these in the console:  1/08/12 1:29:25.982 PM fseventsd[64]: could not open &lt;&lt;/Volumes/RamDisk/.fseventsd/fseventsd-uuid&gt;&gt; (No such file or directory) 1/08/12 1:29:25.982 PM fseventsd[64]: log dir: /Volumes/RamDisk/.fseventsd getting new uuid: 102D7293-F1F1-4640-AA50-D547C365339F  1/08/12 1:29:24.561 PM sudo[1193]:     Aram : TTY=ttys000 ; PWD=/Library/LaunchDaemons ; USER=root ; COMMAND=/bin/launchctl load -w /Library/LaunchDaemons/com.aram.ramdisk.plist  1/08/12 1:40:17.052 PM com.apple.launchd[1]: (com.aram.ramdisk) Throttling respawn: Will start in 8 seconds   It works if I set KeepAlive to true, but then it creates a RAM disk every 10 seconds.  Is there a way to delay the script for 10 seconds before running? Suppose $a_1, a_2,\dots , a_n$ are $n$ positive real numbers with $a_1a_2 \dots a_n = 1$.   Then what is the minimum value of $(1 + a_1)(1 + a_2). . .(1 + a_n)$ ?    I think $(1 + a_1)(1 + a_2). . .(1 + a_n)$ takes its minimum value when $a_1=a_2=\dots=a_n=1$ and thus the minimum value is $2^n$.  I don't know how to prove it. Please help. To show that $\sum a_nb_n$ is absolutely convergent Which is the best way to put function plots into a LaTeX document? Are files created in "/storage/emulated/0" supposed to appear in "/storage/sdcard0"? From what I guess, internal storage is available by every user. If emulated storage is a storage location, made for a specific user, are files created in /storage/emulated/0 supposed to appear in /storage/sdcard0? I assume no, because files that are user created should show up in emulated only, otherwise files created by the user would be available for all other users to see. PGFPlots: Understanding how to draw plots on different layers and arrange them I have gone through previous questions [,,], but I still couldn't figure out how to draw plots on different layers and change their order of drawing.  For this MWE, I would be grateful if I could figure out how to change the order of appearance of the three plots in such a way that the legend entries have the same order while keeping the plots commands/definitions in the same order as much as possible.  \RequirePackage{luatex85} \documentclass{standalone} \usepackage{pgfplots} \pgfplotsset{compat=newest}  \begin{document}  \begin{tikzpicture}     \begin{axis}[             legend style={                 at={([yshift=30pt]0.5,1)},                 anchor=north},             legend columns=-1,             xmin=0, xmax=10,             ymin=0, ymax=10,         ]         %         \addplot [red,      line width = 5pt,   domain=0:10]    {x}; \addlegendentry{$x$}            \addplot [black,    line width = 5pt,   domain=0:10]    {(x-5)^2}; \addlegendentry{$(x-5)^2$}         \addplot [yellow,   line width = 5pt,   domain=0:10]    {10-(x-5)^2}; \addlegendentry{$10-(x-5)^2$}     \end{axis} \end{tikzpicture}  \end{document} Chrome 100% CPU usage, again - software_reporter_tool.exe software_reporter_tool.exe belonging to Chrome running at 100% cpu, fan full speed.  Deleting it doesn't fix anything, because it gets redownloaded again! Disabling "Protect me from bla bla" doesn't make it stop running.  Please anyone have any solutions?