How to replace multiple matching patterns with multiple specified replacement strings in SQL - Oracle
how to replace multiple strings together in Oracle
Find $\lim_{n \to \infty} \left[\frac{(n+1)^{n + 1}}{n^n} - \frac{n^{n}}{(n-1)^{n-1}} \right]$ (a question asked at trivia) My friend's trivia league had this math question:  $$\lim_{n \to \infty} \left[\frac{(n+1)^{n + 1}}{n^n} - \frac{n^{n}}{(n-1)^{n-1}} \right]$$  After computing a few values, one could guess the answer is $e$ = 2.718...But how can we prove that is the limit?  Someone offered up a hand-wavy proof like this:  \begin{align} \lim_{n \to \infty} \left[\frac{(n+1)^{n + 1}}{n^n} - \frac{n^{n}}{(n-1)^{n-1}} \right] &amp; = \lim_{n \to \infty} \left[\frac{(n+1)(n+1)^{n}}{n^n} - \frac{n \cdot n^{n-1}}{(n-1)^{n-1}} \right] \\ &amp;= \lim_{n \to \infty} \left[(n+1)\frac{(n+1)^{n}}{n^n} - n\frac{n^{n-1}}{(n-1)^{n-1}} \right] \\ &amp;= \lim_{n \to \infty} \left[(n+1)\left(1 + \frac{1}{n} \right)^n - n\left(\frac{n - 1 + 1}{n-1} \right)^{{n-1}} \right] \\ &amp;= \lim_{n \to \infty} \left[(n+1)\left(1 + \frac{1}{n} \right)^n - n\left(1 + \frac{1}{n-1} \right)^{n-1} \right] \\ &amp;= \lim_{n \to \infty} \left[(n+1)e - n \cdot e \right] \\ &amp;= \lim_{n \to \infty} e \\ &amp;= e \end{align}  The part about substituting $e$ is hand-wavy since technically this is an indeterminate form of $\infty - \infty$. And using $e$ as as upper bound did not lead me to an easy proof either.  Is there a way to rigorously prove the limit? I tried a few approaches: (a) sandwiching the limit--I could prove $e$ was a lower bound, but I could not find a suitable upper bound converging to $e$, (b) using L'Hopital's rule with no luck, (c) using the mean value theorem--but that also got complicated.  So this is a pretty tough problem to ask at trivia! Is there a way to prove this limit formally?  Sources  Trivia question:   Thread on trivia:   Hand-wavy proof:   Idea for mean value theorem: I really tried hard to do this on my own, but I keep failing ... Using multi-column and multi-row commands confused me. I know some of you might frown upon such a request but I really need help getting this table implemented .. So I'm sorry if I upset anyone.  My preamble has :   \documentclass[12pt,a4paper]{report} \usepackage[lmargin=3.81cm,tmargin=2.54cm,rmargin=2.54cm,bmargin=2.52cm]{geometry} \linespread{1.5}     Is there a way I can convert this from excel to LaTeX form ? I tried an add-in before but it didn't work for me. Also online generators cannot combine cells the way I want them (unless I didn't find a better table generator ? ) Shows "unable to locate package unzip" error I have installed Ubuntu 12.04 server , shows    E:unable to locate the package unzip   the above error is also shown, if I try to install packages also. Can any one help me out to get out from this error. What is the preferred way to mention Stack Overflow from Twitter? I wanted to tweet something on the lines of "Stack&nbsp;Overflow is awesome". When I do this kind of stuff, I usually use a username (for example: ) or a hashtag ()  I found , but it seems it is from someone unrelated with Stack&nbsp;Overflow.  Is there a Twitter account I can reference, or should I use a hash-tag? Should I just point to the site?  Thanks!  (Notice: I've seen lots of questions regarding Twitter and Stack&nbsp;Overflow, but those are mostly about integration/login with Twitter for the users accounts; I'm just asking for a single account for Stack&nbsp;Overflow; probably for announcements and PR, which is different) Using biblatex and Biber, I want my bibliography to say "Ph.D. thesis" (with periods) rather than "PhD thesis" (without). MWE:  \documentclass{article} \usepackage{biblatex} \addbibresource{refs.bib} \begin{document} Hello \cite{testphd} \printbibliography \end{document}   and refs.bib:  @thesis{testphd,   title       = {Thesis Title},   author      = {Surname, Firstname},   date        = {2010},   institution = {Faculty of X, University of Y},   type        = {phdthesis},   location    = {Somewhere}, }   Output:    What's the easiest way to do this? I don't want to change the .bib file ideally. A company is any form of business whether it is small or large. Generally the term &quot;company&quot; indicates a particular kind of business dealing in a specific product. An organisation is the larger form and generally comprises of a number of companies.  Simply, a company is an organization, but an organization is not just a company. An industry is the combination of companies in same line of business. Firm, corporation and business  are synonyms of &quot;company&quot;. An Agency is a particular kind of company, which serves as an intermediary between clients (other companies or individuals).  Is this correct? Creating intuition about Laplace & Fourier transforms How can I convert my Java program to an .exe file? If I have a Java source file (*.java) or a class file (*.class), how can I convert it to a .exe file?  I also need an installer for my program. Extend tourist visa stay in USA due to coronavirus and waive I-539 fee My mom has come to US on a tourist visa and her I-94 expires on the first week of May.   Due to the coronavirus, travel restrictions have been imposed in our home country (India). Also we want to avoid the risk of traveling in flights at this time.  Is there an easy way to to extend her stay in the US by one or two months?  I am aware that we should fill out an  to extend our stay. But in-order to submit the online application it requires a fee of $370.    Is filing I-539 the easiest way to extend her stay at this time? If so, is it possible to waive the fee due to the coronavirus situation?  After filing I-539 should she wait for an approval to continue her stay? Or is the receipt good enough?   Can you please help me with these? Thanks!  [Edit 1]:  With the current situation of the virus, traveling anywhere sounds like a very risky operation, especially for elders.   That is the main reason behind this question. If the US government will allow visitors to overstay until Covid-19 settles down! Calling Non-Static Method In Static Method In Java Has user testing found that the "three horizontal bars" for main menu on mobile is commonly understood? "Three horizontal lines" aka "hamburger icon" seems to be becoming a convention for the "main menu" button, especially on mobile sites:    Has anyone done any user testing of this convention, or got any A/B testing results? (i.e. is there an increase in bounce rate compared to using the word "Menu"?)  I did some quick user testing with wireframes featuring this icon for the main menu. 3 out of 6 people got it and used it. The others did not.  One person in particular had a lot of trouble "getting back to the top" (i.e. restarting their navigation from the top level of the site) as they didn't know about the convention, or that the logo would link to the home page.  I guess it will be different for different demographics - users of Facebook on mobile probably know it.  Anyone got any findings they can share? How to compute the size of the allocated memory for a general type The only things I've found so far are a cart method (which ceased working in 1.6), a dispenser method (utilizing the decay on dropped items, but this requires occasional feeding), and a binary counter (which won't work for a single input but rather a fluctuating one).  I want to have a circuit that when I apply an input signal, the output signal doesn't change for 2 to 5 minutes.  When the input turns off, I again want a 2 to 5 minute delay.  I could accomplish this with (roughly) 240 to 600 redstone repeaters, but this is far in excess of being useful.  The only method I can think of, but would require a XOR gate (on the button-input and final output) to start and stop a clock attached to a binary counter.  While I can make room for a device of this size, I was hoping for something simpler. Does the cross-entropy cost make sense in the context of regression? Does the cross-entropy cost make sense in the context of regression (as opposed to classification)? If so, could you give a toy example through TensorFlow? If not, why not?   I was reading about cross-entropy in  by Michael Nielsen and it seems like something that could naturally be used for regression as well as classification, but I don't understand how you'd apply it efficiently in TensorFlow since the loss functions take logits (which I don't really understand either) and they're listed under classification Proof of Frullani's theorem "+-=,;..." math characters in DejaVu Sans (with mathspec) the following MWE  \documentclass{minimal} \usepackage{mathspec} \setmainfont{DejaVu Sans} \setmathsfont(Digits,Latin,Greek){DejaVu Sans} \setmathrm{DejaVu Sans} \begin{document} \(\mathrm{e}^{\mathrm{i}\pi}=-1\) = -1 \end{document}   typesets with xelatex into    How can I turn the = and - signs in math mode to DejaVu Sans ? I've noticed a MATCH SIMPLE and MATCH FULL, but I don't understand what they do. I see default is MATCH SIMPLE; but, how do the other MATCH clauses to the FOREIGN KEY constraint function? What about lowering the edit character limit for characters in code snippets? , to correct a misspelled library enum in an answer. Since the edit was only one character, I also had to add a superfluous sentence to get over the character limit required to edit a post.  I've hit this problem before in other edits, always in code snippets. Since the edit limit exists to prevent trivial edits, and since there are many cases where one character code edits are not trivial (= to == etc), would it make sense to have a lower edit minimum inside code snippets? I read a very special book a few years back. We follow a boy who lives in a world where, if one moves far enough in a direction, that person gets distended and changed in size.   The boy works on laying tracks for the train, on which his city is. The city has to continually keep moving or it also will get squashed.   It's like a world like if one end is pinched and then dragged out like a piece of rubber string or bubble gum.   The book is not older than 10 years I think.  Hope I was clear enough... How to install MariaDB?