Finding $\displaystyle \lim_{y\rightarrow \infty}\bigg[\frac{y}{e}-y\bigg(\frac{y}{y+1}\bigg)^y\bigg]$   Attempt: Put $\displaystyle y=\frac{1}{z}$ . Then $\displaystyle \lim_{z\rightarrow 0}\bigg[\frac{1}{ze}-\frac{1}{z}\bigg(\frac{z}{z+1}\bigg)^{\frac{1}{z}}\bigg]$  Could some help me to solve it, thanks
How can I compute the following limit, and is there a general method to resolve problems of this type?  $$\lim_{x\to\infty}x\left[\left(1+\frac{1}{x}\right)^x-e\right]$$
Get rid of the question ban on Meta; suspend actively harmful users manually For example I want to use \iint from ams package  and also mathabx package in one file together. Actually I want a command that neutralizes ams package effect and replace it with mathabx package effect from here on in my file. Thanks for your responsibility.  This is my example minimal file:  \documentclass[12pt,a4paper]{report} \usepackage{amsmath}  \usepackage{mathabx}  \begin{document} i want this one in ams style:        \[ \iiint\,\iiint\, \iiint\,\oint\, \] text text text text text text text text text text text text   and this one in mathabx style:   \[ \iiint\,\iiint\, \iiint\,\oint\, \]   but both of them are the same and i don't like it ..... \end{document} Disk storage graphic and usage amount inconsistent? Sum $\frac{1}{6} + \frac{5}{6\cdot 12} + \frac{5\cdot 8}{6\cdot 12\cdot 18} + \frac{5\cdot 8\cdot 11}{6\cdot 12\cdot 18\cdot 24}+\ldots$ A series is given as follows   $$\frac{1}{6} + \frac{5}{6\cdot 12} + \frac{5\cdot 8}{6\cdot 12\cdot 18} + \frac{5\cdot 8\cdot 11}{6\cdot 12\cdot 18\cdot 24}+\ldots$$  Can you give me hints to get started finding its value? Thanks. Can I make a public directory under a private directory? I have a personal folder /a/b on the server with permission 700. I don't want others to list the contents in /a/b. The owner of /a is root.  Now I need to open the full authorities of directory /a/b/c to all users.  I changed the permission of /a/b/c to 777 but it is still inaccessible for others. Is it possible to combine processing power of 2 computers? How to find and replace a string by increasing its numerical part? In school, we just started learning about trigonometry, and I was wondering: is there a way to find the sine, cosine, tangent, cosecant, secant, and cotangent of a single angle without using a calculator?  Sometimes I don't feel right when I can't do things out myself and let a machine do it when I can't.  Or, if you could redirect me to a place that explains how to do it, please do so.  My dad said there isn't, but I just had to make sure.  Thanks. Real Analysis Riemann Integration - Strict Monotonicity for Integrals If $f,g$ are Riemann integrable on $[a,b]$, and $f(x) &lt; g(x)$ for all $x \in [a,b]$, prove that $$ \int_a^b f(x) \,dx &lt; \int_a^b g(x) \,dx$$  This is a strict inequality. I know how to prove the monotonicity of integrals with the non strict inequality, but I am not sure how to do this. Negative energy levels in the diagram for a hydrogen atom The higher the number of the shell (n), the higher is the energy level of the electron. However, why was it necessary to have negative values. So for example, when $n=1$, the energy could be $5 eV$ and for $n=2$, $6 eV$... having positive values could also have supported the idea that as $n$ increases, energy of electron increases. What is the point of having negative numbers, does it somehow aid calculations? I'm stuck with an uninstallable module. Drupal insists that there are Fields pending deletion and that the module can not be uninstalled. I've run cron zillion times already as advised for such situations but without success. Cron runs fine, but drupal insists that still, Fields pending deletion.  Visiting /admin/reports/fields gives no clues - the fields provided by that module are not listed. I even tried using drupal console to uninstall module with --force switch, but also without success.  I also tried drush field-info in hope to get some clues, but that's apparently not yet implemented as drush 8.1.2 gives fatal error:     Call to undefined function field_info_fields().   How do I make drupal delete those fields that pending deletion? Do I have to do this manually in database?  I've seen few tables like field_deleted_data_f5e7b87e32 or field_deleted_revision_be01eddd10 but they are all empty. Is that even relevant? Why does $PSL(2,\mathbb C)\cong PGL(2,\mathbb C)$ but $PSL(2,\mathbb R) \not\cong PGL(2,\mathbb R)$? Why does $PSL(2,\mathbb C)\cong PGL(2,\mathbb C)$ but $PSL(2,\mathbb R) \not\cong PGL(2,\mathbb R)$? I don't understand why su - is preferred over su to login as root. Let's have breakfast    Let's have a good breakfast      I've learned that indefinite articles aren't used before uncountable nouns, so why is a used before the adjective "good" here?    Is there an exception to the rules or is it wrong? How do I select multiple elements and a class in JQuery At the very end of Deathly Hallows, after Harry repaired his own wand with the Elder Wand, he tells Dumbledore's Portrait in the office:     “I’m putting the Elder Wand,” he told Dumbledore, who was watching him with    enormous affection and admiration, “back where it came from. It can stay there. If I die a    natural death like Ignotus, its power will be broken, won’t it? The previous master will    never have been defeated. That’ll be the end of it.   Now, this seems incredibly foolish to me.  "The previous master will never have been defeated" would only have been assuredely true if Harry had died right after depositing the Elder Wand back into Dumbledore's Tomb.   If not, Harry (the Wand owner) would still be alive, and at the risk of being Disarmed (as was shown with Harry and Draco Malfoy, it doesn't matter if the Elder Wand's owner is defeated by death or simple disarming, AND it's not even required that the Disarming would involve the Elder Wand!).  So, if Harry merely put the Elder Wand back into the Tomb, and some years later, someone would disarm him (or, even worse, kill him) - then that someone would become the Elder Wand owner, either by accident or by design:    By accident - Harry is likely to get into plenty of magical duels in the future. Even discounting friendly one (teaching people the Expelliramus), he plans on becoming an Auror!  By design - plenty of people have been in the Great Hall hearing Harry explaining to Voldemort that he, Harry, was now the owner of the Elder Wand, so the fact of his ownership would most assuredly NOT remain a secret, inviting countless people tempted by owning the Deathstick to hunt Harry down. Oh, and the location is now also known!   So "its power will be broken" is quite unlikely to come true!  Is Harry hopelessly wrong? Or am I missing something in the above logic? Was this addressed in canon/JKR info? Is there an easy way to log all commands executed, including command line arguments? I am trying to find how to log a specific instantiation of rrdtool to see whether the path it is receiving is incorrect.  I know I could wrap the executable in a shell script that would log the parameters, but I was wondering if there was a more kernel-specific way to monitor for that, perhaps a filesystem callback that sees when a particular /proc/pid/exe matches a given binary? What program can be used to package software into one executable? What do you call the symbols list on a map? Every map has symbols that describe things. In the corner of a map, there is a list that explains what each symbol means.  What is the name of that list? (What title should I put above this list)? Seeing close-vote details if I've already voted If I've already voted to close a question, it would still be nice to see the details of others' votes — the suggested migration if it's being marked as off topic, or the suggested duplicate if it's being marked as an exact duplicate, for instance. Instead, I only see "You have already voted to close this question" and the overall category.