How do you find this limit using algebra?  $$ \lim \limits_{s\to 16} \frac{4-\sqrt{s}}{s-16} $$  By graphing I get 1/8.
Find $ \lim\limits_{ x\to 100 } \dfrac { 10-\sqrt { x } }{ x-100 }$  (without using a calculator and other machines...?)
Modules over commutative rings I'm trying to get my head around modules, and there's a problem that's bothering me regarding scalar multiplication from the left vs from the right.  In many books/articles I've read, the author may refer to a left $R$-module $M$, and then continue to talk of terms such as $xr$, where $x\in M$, $r\in R$. What is right scalar multiplication in a left module? Does it even make sense to talk about it?  I've been trying to show that over a commutative ring, right scalar multiplication and left scalar multiplication are the same thing, but I've not managed it so far. I've googled it to no avail, and I can't see why the distinction between left and right modules disappears when the base ring is commutative.  Thanks for any replies! print IP address with interface name I want to show the IP address like below  lo : 127.0.0.1  eth0 : 192.168.5.123 eth1 : 192.172.0.212 wlan0 : 10.1.0.124   I'm able to print all IP address by ifconfig | awk '/inet addr/{print substr($2,6)}'. But it is only printing the IPs. Every system have their own interface names and addresses. So my script has to show their interfaces with respect to IP addresses. Alarm is working even when the phone is powered off I just discovered that if I set the alarm clock and then power off the phone (by holding the power button and then selecting "Power Off") the alarm will still go off when the time comes.  Is this expected behavior? It makes me feel like "power off" doesn't actually power off the phone.  I have a Huawei Y530-U051 running android 4.3. PSTricks will not compile \documentclass[12pt]{article} \usepackage[paperheight=9in,paperwidth=13.24in,margin=0in]{geometry} \usepackage{pstricks} \usepackage{graphicx} \begin{document} \thispagestyle{empty} \psset{unit=1in} \begin{pspicture}(13.24in,9in) \psframe[fillstyle=solid,fillcolor=Maroon](0,0)(13.24,9)  \end{pspicture}  \end{document}   I am following a tutorial outlined here:   I am following the Robbers book.  Everything seems fine until I paste the \psframe[fillstyle=solid,fillcolor=Maroon](0,0)(13.24,9)  What could be the problem? How to find relevant and new open research topics? When defining a method on a class in Python, it looks something like this:  class MyClass(object):     def __init__(self, x, y):         self.x = x         self.y = y   But in some other languages, such as C#, you have a reference to the object that the method is bound to with the "this" keyword without declaring it as an argument in the method prototype.    Was this an intentional language design decision in Python or are there some implementation details that require the passing of "self" as an argument? I have an ex who has posted nude photos of me online in the past, linked to my online social media, and posted my full name and where I live. I am concerned he may do so again once he finds out I'm now in a PhD program (he's very jealous of any success I have), and may link to my school bio page, or worse.   Revenge porn is illegal in my state, and the case against him is currently pending. I have also gotten the photos taken down with a DMCA letter (I hold the copyright over the photos in question). At this point, I am concerned with how a future attempt could affect my career.  I can handle the embarrassment now that I've been through it once, so if that's the biggest concern, I can deal. I just don't want to lose a career over it, given how small academia really is and how a reputation might follow one around.  My question is, if I don't change my name (I've considered this, assuming I can keep him from finding out) and my photos are circulated and discovered by faculty or students, how likely am I to be thrown out of my PhD program or later lose a job as an untenured prof? Is a name change worth it?   (If it makes any difference, they are essentially just topless portraits; I'm not engaged in any sexual activity or anything weird, and were taken 10 years ago when I was very young and foolish.) Need to draw a flowchart as in the image below with some arrows I have problem with the feed back from bottom block to on top of top block. Can anyone help? Crick’s Central Dogma — Counter Cases This is the problem I am currently having trouble with:  If $\lambda_1$ and $\lambda_2$ are eigenvalues of matrix  $$         \begin{bmatrix}         a &amp; b\\         c &amp; d\\         \end{bmatrix}$$prove that $\lambda_1^2$, $\lambda_1\lambda_2$ and $\lambda_2^2$ are eigenvalues of matrix $A$.     $$A=\begin{bmatrix}     a^2 &amp; ab &amp; b^2\\     2ac &amp; ad+bc &amp;2bd\\     c^2 &amp; cd &amp;d^2\\     \end{bmatrix}$$  What have I considered so far:   I tried to find characteristic polynomial of first matrix and then find the roots which would be $\lambda_1$ and $\lambda_2$. I was hoping I can make a connection with characteristic polynomial of matrix $A$, but it got too complicated and did not seem like the right idea. Since there are two eigenvalues for first matrix, there are two eigenvectors. I thought about somehow using $A\vec v_i=\lambda_i\vec v_i$, where $i=1,2$  Also, I thought about finding a connection between these two matrices. What I see is that the sum of elements of first and second column, of first matrix, are $(a+c)$ and $(b+d)$, respectively.  Sum of first, second and third column of matrix $A$ are $(a+c)^2, (a+c)(b+d)$ and $(b+d)^2$. Now, if I could assign $\lambda_1$ and $\lambda_2$ to $(a+c)$ and $(b+d)$, then I would get that sum of first, second and third column of matrix $A$ are $\lambda_1^2$, $\lambda_1\lambda_2$ and $\lambda_2^2$, but what would be next?   I thought it would be good to combine 2. and 3rd idea, but I am not making any progress.  I appreciate any help. This is in very common use on the internet. I just read this:     "[The] hotel employee walks in, I say "uh, puppy" and she just NOPEd the [heck] out of the room."   This is often done by adding 'd to the word. Save entire process for continuation after reboot How do you take profit from stock trading while keeping capital invested? A google search gives number of methods to hide ALL tabs in chrome , but I want to hide 1 particular tab / change the display name of that tab.   Reason: I have an online music playing website open, which keeps showing tracks in the tab name and I just want to remove it from view of my work. How to avoid WSP deployment globally using Visual Studio 2010? How can we avoid the Globally Deployment of a WSP using Visual Studio 2010? I can't find my other HDD New Ubuntu user here... I have Ubuntu on my 250GB SSD and I have another 500GB on my laptop that Ubuntu can't find. I'm not sure where or how to start finding it. Can I choose to use only Shapiro-Wilk? Wrapping a mesh around point cloud with cavities In the recently launched trailer of Fantastic Beasts: The Crimes of Grindelwald, there are people Apparating inside Hogwarts grounds.                                  As these people later question Professor Dumbledore, it seemed they were Ministry officials.  Have we ever encountered such Apparition before? Or, was this anti-Apparation charm put into place in recent times? How to raise a complex number to the power of another complex number? How do I calculate the outcome of taking one complex number to the power of another, ie  $\displaystyle {(a + bi)}^{(c + di)}$?