I would like to find a solution $x$ for $x^x = c$ where $c$ is a positive constant.  Firstly I'm looking for an approximative solution when $c$ tends to infinity.  Thank you in advance
Given that   $x^x = y$; and  given some value for $y$   is there a way to expressly solve that equation for $x$?
equivalent date from GNU to solaris Handling very large numbers in Python Proof of $1+x\leq e^x$ for all x? Justifying the Normal Approx to the Binomial Distribution through MGFs Would absolutely love if someone could help me with this question, in a step by step way to help those who are uninitiated to Statistics and Mathematics.   So, I am trying to "prove/justify" through MGFs how as n(the sample size) increases and goes to infinity, a standardized binomial distribution converges to the Standard Normal Distribution. So in the beginning we have $X_n $~$ Bin(n,p)$ then we standardize this $R.V.$ by subtracting the mean $E(X_n)=np$ and dividing by the $SD$ which is $np(1-p)$. After doing this, we get a new $R.V.$ with $mean=1$ and $variance=SD=1$. It is the distribution of this standardized quantity that converges to a fixed distribution, correct? Namely the Standard Normal Distribution. Let's call the standardized version of $X_n$, $Z_n$.   I think what we need to do is to find the MGF of $Z_n$ and show that this MGF becomes the Standard Normal Distribution's MGF as the sample size $(n)$ heads toward infinity. Now $Z_n$ is a function of $X_n$ which we know the MGF of which is $(1-p+pe^t)^n$.   Now I know that $Z_n$ is a linear transform and that we should be able to use this to simply the MGF but I don't understand how the course notes do it, mostly because they skip a lot of steps and it is difficult to follow. There is also a Taylor Series Expansion for the exponential that I am confused about although I do understand the concept of the series expansion.  Help would be greatly appreciated! I would love assistant in exactly how we can prove this via MGF.   Thanks so much in advance :) Edit file based on existence of a string I have an input file, say, file1, which appears as follows:  WRITE=2 START=1 SMEAR=0 MIN=6 MAX=100   My problem is to search for the string SMEAR and if the string exists replace the entire line with SMEAR=-5. However, if the SMEAR does not exist, then I need to insert a new line SMEAR=-5. Ultimately the line SMEAR=-5 should appear only once. I can replace the string using sed:   sed -i '/SMEAR/c\SMEAR=-5' file1   Or I can insert the string as a new line    sed -i '10i SMEAR=-5' file1   But how can I combine them based on the existence of the string in the file?  EDIT: Also it would be helpful if I can pass the value of SMEAR as a variable. Factoring $-3x^2 - 2xy + 8y^2 + 11x - 8y - 6$ On my Toshiba Encore 8 Tablet I noticed that the CPU usage is very high. In Taskmgr / ProcessExplorer, I can see that OneDriveSetup.exe is hogging 1 CPU cores heavily for hours.    How an I solve this hang and finish the OneDrive Update? Exclude a view from master layout? Steam not opening in Ubuntu 16.04 LTS I have never used Ubuntu or any other Linux OS before last Friday. For all I know, I might have installed Ubuntu wrong and be missing a component. I would prefer if you use simplest terminology possible, but I'm OK with doing a bit of googling if need be. I just installed Steam for Ubuntu 16.04 but it won't open when I click on it in the launcher. The icon flashes for a few seconds, stops and then nothing happens. I looked in the system monitor and steam shows up there but ending the process and trying again does nothing. I heard trying to open apps that aren't working through the terminal tells you what the error is so I tried that and I got this:  Running Steam on ubuntu 16.04 64-bit STEAM_RUNTIME is enabled automatically Installing breakpad exception handler for appid(steam)/version(0) libGL error: unable to load driver: radeonsi_dri.so libGL error: driver pointer missing libGL error: failed to load driver: radeonsi libGL error: unable to load driver: swrast_dri.so libGL error: failed to load driver: swrast   Please help I just want to play CS:GO again. Show that one-sided limits always exist for a monotone function (on an interval) Show that one-sided limits always exist for a monotone function on an interval $[a,b]$.  Me attempt:  1) If a function is monotone on an interval $[a,b]$, then $f(a)\le f(x) \le f(b)$ for $x\in[a,b]$. Therefore if there exists left-hand (right-hand) limit of this function at a given point, then it must be finite. Now we must show that a both left-hand and right=hand limits exist. We use the fact that if we take a sequence $(x_n)\rightarrow c^{+} \in [a,b]$ then $f(x_n)$ is bounded and monotone and therefore it is convergent. How to convert an MKV to AVI with minimal loss To convert an MKV to AVI, I do two things. The first thing I do is this:  ffmpeg -i filename.mkv -vcodec copy -acodec copy output.avi   or this:  ffmpeg -i filename.mkv -sameq -acodec copy output.avi   Either of these will convert the MKV to an AVI, but the problem is that the video does not play smoothly for some reason. That's fine though, because if I do one more thing it gets fixed:  ffmpeg -i output.avi -vcodec mpeg4 -b 4000k -acodec mp2 -ab 320k converted.avi   After I do this then the file plays without problem. I had success doing it this way for one file, but then I tried it on another file, and there is a slight, but noticeable loss in video quality. This is the output I get when doing the second step:  FFmpeg version 0.6.1, Copyright (c) 2000-2010 the FFmpeg developers   built on Dec 29 2010 18:02:10 with gcc 4.2.1 (Apple Inc. build 5664)   configuration:    libavutil     50.15. 1 / 50.15. 1   libavcodec    52.72. 2 / 52.72. 2   libavformat   52.64. 2 / 52.64. 2   libavdevice   52. 2. 0 / 52. 2. 0   libswscale     0.11. 0 /  0.11. 0  Seems stream 0 codec frame rate differs from container frame rate: 359.00 (359/1) -&gt; 29.92 (359/12) Input #0, avi, from 'output.avi':   Metadata:     ISFT            : Lavf52.64.2   Duration: 00:04:17.21, start: 0.000000, bitrate: 3074 kb/s     Stream #0.0: Video: mpeg4, yuv420p, 704x480 [PAR 229:189 DAR 5038:2835], 29.92 fps, 29.92 tbr, 29.92 tbn, 359 tbc     Stream #0.1: Audio: vorbis, 48000 Hz, stereo, s16 Output #0, avi, to 'converted.avi':   Metadata:     ISFT            : Lavf52.64.2     Stream #0.0: Video: mpeg4, yuv420p, 704x480 [PAR 229:189 DAR 5038:2835], q=2-31, 4000 kb/s, 29.92 tbn, 29.92 tbc     Stream #0.1: Audio: mp2, 48000 Hz, stereo, s16, 320 kb/s Stream mapping:   Stream #0.0 -&gt; #0.0   Stream #0.1 -&gt; #0.1   I just used arbitrarily large settings on the second step and it worked nicely before but not in this case. What settings should I use? Displacement currents, aren't really currents? Can Recovery Mode install OS X onto a blank SSD? I want to install a new Solid State Drive (SSD) into the Mac. Can I just build in the SSD, start the MacBook in Recovery Mode and install OS X from there on?  After reading a lot on the internet I still have some doubts…  My HDD crashed, I can't repair it using disk utility or the fsck methods as mentioned on the internet.  According to  it should be possible.  I know how to replace the HDD with the SSD. I would go for the Samsung 850 EVO SSD - 500GB. My Mac is a MacBook Pro Mid 2012, model A1278. $$\begin{align} 2+2 &amp;= 4 - \frac92 +\frac92\\ &amp;= \sqrt{\left(4-\frac92\right)^2} +\frac92\\ &amp;= \sqrt{16 -2\times4\times\frac92 +\left(\frac92\right)^2} + \frac92\\ &amp;= \sqrt{16 -36 + \left(\frac92\right)^2} +\frac92\\ &amp;= \sqrt {-20 +\left(\frac92\right)^2} + \frac92\\ &amp;= \sqrt{25-45 +\left(\frac92\right)^2} +\frac92\\ &amp;= \sqrt {5^2 -2\times5\times\frac92 + \left(\frac92\right) ^2} + \frac92\\ &amp;= \sqrt {\left(5-\frac92\right)^2} +\frac92\\ &amp;= 5 + \frac92 - \frac92 \\ &amp;= 5\end{align}$$  Where did I go wrong I want to mount the device /dev/sda3 to the directory /foo/bar/baz. After mounting the directory should have the uid of user johndoe. So I did:  sudo -u johndoe mkdir /foo/bar/baz stat -c %U /foo/bar/baz johndoe   and added the following line to my /etc/fstab:  /dev/sda3 /foo/bar/baz ext4 noexec,noatime,auto,owner,nodev,nosuid,user 0 1   When I do now sudo -u johndoe mount /dev/sda3 the command stat -c %U /foo/bar/baz results in root rather than johndoe. What is the best way to mount this ext4-filesystem with uid johndoe set? Why is the last digit of $n^5$ equal to the last digit of $n$? What is a Seaman's book, and can it really replace a passport? What is a "Seaman's book", and can it really replace a passport for some or all immigration purposes?  Even Wikipedia the all-knowing does not seem to know, although it contains many tantalizing references.  :     Seaman deserters may not have a passport but rather hold a Seaman's Book, (a national identity document issued to professional seamen that contains a record of their rank and service career).   :     Possession of one of the following documents is sufficient to demonstrate [right to abode] ...         Hong Kong Seaman's Identity Book I need to get a nice picture about how electron moves around nucleus? I find concept of probability and orbitals quite difficult to understand? Is phonetic typing for Tamil available in Ubuntu 12.04?  How can I install it? Let $U,W$ be subspaces of a vector space $V$. Show that   $$\dim(U)+\dim(W)=\dim(U+W)+\dim(U\cap W)$$   Hint: Show that the map given by $L:U×W\to V$ given by $L(u,w)=u-w$ is linear.   I can show that $L:U×W\to V$ given by $L(u,w)=u-w$ is a linear map. I also know that the dimension of $U×W$ is $\dim(U)+\dim(W)$. What do I do next? Any hints?