I played with the natural logarithm (injectivity) and ended with a Riemann sum. When n is converging against infinity, the sum converges against -1: $$\int_{0}^1 \log(x) \, \mathrm{d} x = \lim_{x\to 0} 1 \cdot \log(1)-1 -\left( x \log(x)-x\right)$$ I do not know if that is correct. Please help!
I am asked to determine if a series converges or not:  $$\displaystyle\sum\limits_{n=1}^{\infty} \frac{(2^n)n!}{(n^n)}$$  So I'm using the $n$th root test and came up with $\lim_{n \to {\infty}}\frac{2}{n}\times(\sqrt[n]{n!})$ I know that the limit of $\frac{2}{n}$ goes to $0$ when $n$ goes to infinity but what about the $(\sqrt[n]{n!})$?
In what order do multiple readied actions with the same trigger resolve? My players have been scheming with rapid entry tactics for the megadungeon I've recently started running. Unfortunately, the monsters are aware of the adventurers, and this has lead to a weird question of priority. Given the following situation (which I'm pretty sure is going to happen next session in some form or another) what happens?     Alice the adventurer readies an action; if her teammate Carlos opens   the door, she's going to throw the alchemists fire through the door,   which should do enough damage to kill any goblins hiding there.      Meanwhile, on the other side of the door, Bob the goblin is lying in   wait. He readies an action; if the door opens, he's going to hit the   switch to open the trapdoor in the next room, which should drop any    pesky adventurers into a pit with spikes at the bottom.      Carlos opens the door.   I know what happens when , but what happens when multiple readied actions get triggered at the same time? My guess would be an opposed reflex save or initiative check of some kind to see who goes first, but that's entirely just intuition speaking. The rulebook doesn't seem to speak to the issue. Calling a parent window function from an iframe How do I view 'git diff' output with my preferred diff tool/ viewer? When I type git diff, I want to view the output with my visual diff tool of choice (SourceGear "diffmerge" on Windows). How do I configure git to do this? I've been having this issue for a while where I come to open the Terminal and I'm met with this:  Login incorrect login: _   I've already deleted the com.apple.terminal.plist to no avail. The really interesting thing is that sometimes it works, maybe 1 in 50 times. I literally have no idea what might be causing it and after searching the web for the better part of half a day it seems everyone else's issues are fixed when they delete the plist file.  How do I sort this out? I've tried running different shells (bash and zsh), but I still get this log in screen.  Also when I use Activity Monitor, I can see there is no shell running just the login. Input field for decimal property My VF tags:  &lt;apex:column &gt;     &lt;apex:facet name="header"&gt;Sales Price&lt;/apex:facet&gt;     &lt;apex:inputText value="{!prod.SalesPrice}"/&gt;     &lt;/apex:column&gt;   Controller code:  public string SalesPrice{get; set;} oli.UnitPrice =decimal.valueOf(pi.SalesPrice);   It works when a user insert 15 and 15.00 but it doesn´t with 15,00(comma).  I m using apex:inputText linked to a controller apex property because apex:inputfield is not allowed.  I´ve tried with apex:input with type=number but it doesn´t look good, (small button to increase/decrease inserted value). Is there another Visualforce tag that i can use with a property? Is the only solution to replace comma with dot in the controller? There was a film from the 80s in which young people can teleport anywhere they can think of.   These guys are recruited to do studies with, maybe by the government or a secret company which wants the take advantage of their abilities.   I saw it on cable TV around 1990-1997.   Any clues? What does the second column in the output of 'ls -n' mean? Comma usage with compound sentences {actually compound predicates as per Rob's answer} Rule 101 of compound sentences is that a coordinate conjunction must be accompanied by a comma most of the time when joining independent clauses, yet I stumble across sentences all that time that seem to abuse this rule. Normally, it's a case of the subject not being present in the second clause, as in the following example:      "They usually start out as an abbreviation, but turn into acronyms   when they become well known."   (taken from the Oxford Style Manual)   To me, this comma cannot be correct because the clause after the comma doesn't contain a subject and therefore cannot be independent (right?). As far as I'm concerned, it's not the 'Comma to set off a contrast rule because I can find plenty of other where 'and' is used and the subject's missing in the second clause.  what's the deal here?   Thanks in Advance for any responses I may receive! Why does a monopole not radiate energy in electodynamics? I'm trying to find a discontinuous linear functional into $\mathbb{R}$ as a prep question for a test. I know that I need an infinite-dimensional Vector Space. Since $\ell_2$ is infinite-dimensional, there must exist a linear functional from $\ell_2$ into $\mathbb{R}$. However, I'm having trouble actually coming up with it.   I believe I'm supposed to find an unbounded function (although I'm not sure why an unbounded function is necessarily not continuous; some light in that regard would be appreciated too), so I thought of using the vectors $e^i$, which have all entries equal to zero, except for the $i$-th one. Then, you can define $f(e^i)=i$.  That'd be unbounded, but I'm not sure if it'd be linear, and even if it is, I'm not sure how to define it for all the other vectors in $\ell_2$.   A friend mentioned that at some point the question of whether the set $E=\{e^i:i\in\mathbb{Z}^+\}$ is a basis would come up, but I'm not sure what a basis has to do with continuity of $f$.   I'm just learning this topic for the first time, so bear with me please.   The space of sequences that are eventually zero (suggested by a few people) turned out to be exactly what I needed.  It also helped to cement the notions of Hamel basis, not continuous, etc. How to reorder /etc/resolv.conf at load time I have a CentOS system that retrieves its upstream DNS servers via DHCP.  I want to run DNSMasq on this box and use it as a server to resolve some hostnames for development.  The problem is when my system starts, the upstream DNS servers are loaded into /etc/resolv.conf and THEN the DNS1 entry from my ifcfg-enp0s3 setup gets loaded.   That's a problem because when I query for the internal dev names, it tries to go out to the upstream DNS server instead of checking DNSMasq first.  I need the DNSMasq server to be at the TOP of the /etc/resolv.conf and the dhcp loaded ones at the bottom of the resolv.conf so that DNSMasq will work properly.  Any simple way to do that? I looked around but did not find that anyone has asked this before, but what are the fonts that are standard/recommended while writing academic reports/papers? Easy way to use variables of enum types as string in C? Here's what I am trying to do:    typedef enum { ONE, TWO, THREE } Numbers;   I am trying to write a function that would do a switch case similar to the following:   char num_str[10]; int process_numbers_str(Numbers num) {   switch(num) {     case ONE:     case TWO:     case THREE:     {       strcpy(num_str, num); //some way to get the symbolic constant name in here?     } break;     default:       return 0; //no match   return 1; }   Instead of defining at every case, is there a way to set it using the enum variable like I am trying to do above? Show that a ring is commutative if it has the property that ab = ca implies b = c when $a\neq 0$ Show that a ring is commutative if it has the property that ab = ca implies b = c when $a\neq 0$.   This is my proof to show that a ring is commutative if it has the property that ab = ca implies b = c.  We need to show that if x, y ∈ R then xy = yx. Let a = x, b = yx and c = xy. Then ab = x(yx) = (xy)x = ca. Thus, by the hypothesis, b = c, or xy = yx. Thus, for x, y ∈ R we have xy = yx.   How would I show when $a\neq 0$? Proof: How many digits does a number have? $\lfloor \log_{10} n \rfloor +1$ I read recently that you can find the number of digits in a number through the formula $\lfloor \log_{10} n \rfloor +1$ What's the logic behind this rather what's the proof? which app triggers the "Windows features" dialog? I keep getting this window titles "Windows Features" It then says that:     An app on your PC needs the following Windows feature:      .NET Framework 3.5 (Includes .NET 2.0 and 3.0)   and I can choose to install or skip (being warned that my apps might not work correctly).  There is also a "telll me more about this feature" link but it explains about the .NET framework.  I want to know if there is a way for me to know which application is it that asks for this feature as the window just keeps popping out of the context of activating a new app...  This all started just a few days ago after some unattended update on my windows 10. How to make the term "page" show in the Glossary list? Is there a systematic way of solving cubic equations? In my text book, to solve cubic equations, I need to    find by trial &amp; error what $f(a)$ will make the equation 0. The factor will be $(x-a)$ then the other factor will be $Ax^2+Bx+C$ then I can solve using compare coefficient   But for te first part, is there any other way apart from trail &amp; error? Or is there some technique to guess the factor of an equation?   The question I am currently doing happens to be $2x^3+3x+4=9$   UPDATE:  $2x^3+3x+4=9$ should be $2x^3+3x+4=9x^2$   UPDATE 2  So I am going to try substituting   $x=\pm{1}, \pm\frac{1}{2}, \pm{2}, \pm{4}$  When $x=-\frac{1}{2}$, one of the provided answers,   $2(−0.5)^3−9(−0.5)^2+3(−0.5)+4=-18.75\neq 0$   did I make a mistake? What is a simple way to create a binary relation symbol on top of another? What is a simple way to have \ll on top of \gg with equal size and vertically center aligned and have them work as a binary relation symbol like \lessgtr? The commands \underset and \overset cannot be used because they do not treat the two symbols equally, and they do not vertically center. I'm reading a lot of documentation on sed, and am still stumped on my particular use case.  I want to replace this line in a conf file with my own line:  Replace this line: #maxmemory &lt;bytes&gt; with: maxmemory 26gb  This is what I tried:  sed s/maxmemory.*bytes.*/maxmemory 26gb/ /etc/redis/redis.conf  I get the error: sed: -e expression #1, char 30: unterminated `s' command  Which stumps me because I don't know what that means. So my question is:  How can I accomplish what I want? What does that error mean? (so I can learn from it)