Calculating $ \lim_{n\to \infty} (1+\sin({1}/{n}))^{n}$ without L'Hopital or series expansions
What is the limit of
I know when evaluated it gives one but I can't figure out how to prove it.  Can anyone help? I believe it requires L'Hopitals rule and taking a natural log but i cannot figure out the exact math. Sneak Damage multiplier: Does it apply to magical damage too? Example:   Dagger 1 = 18 Damage, 25 Shock  Dagger 2 = 33 Damage, no magic  Using the above, when I sneak attack and have the 15x multiple then is the damage caused by Dagger 1 is (18+25)*15 or (18*15)+25 ?  Same question with bows and arrows, does the multiplier apply to potion damage or/and the magical(enchanted)?  In other words, do the multipliers apply to the base damage only or to the final damage being caused by the weapon (base+magical+skill+potion+perks etc)?  I am confused. :-? Show that an operation being commutative is a structural property Top-bar hat misplaced Rotating a table so that at least two name cards are correct Counter with 4 flip flops jk synchronous from 3 to 13! I have to create a counter with 4 flip flops jk synchronous. The counter shall count in this order: 3 to 13 and then to 3 to 13 and so on..  I have to use logisim simulator.   Ok. So i think its solved. I realized that the circuit needs to start at 0 ou 1 and stabilize after the 13 and then it goes to 3. Thanks for your help.  Hope this will help for somebody else too.  Thank you all for your help! According to the documentation  in order to retrieve a list of picklist values for an object we need to pass in a Record Type Id which can be retrieved using the getObjectInfo method.   The issue is that these are both wire functions and I cannot figure out how to chain these methods.  If I try code like the following:  getObjectInfo({ objectApiName: ACCOUNT_OBJECT })             .then(result =&gt; {                 return getPicklistValues({recordTypeId: result.defaultRecordTypeId, fieldApiName: TYPE_FIELD});             })             .then(result =&gt; {                 this.picklistValues = result.data             })             .catch(error =&gt; {                 this.error = error;             });   I get an error      render threw an error in 'c:getpicklistexample' [Imperative use is not   supported. Use @wire(getObjectInfo).]   If I try something like   @track rtId;      @wire(getObjectInfo, { objectApiName: ACCOUNT_OBJECT })     handleResult({error, data}) {         if(data) {             this.rtId = data.defaultRecordTypeId;         }     }      @wire(getPicklistValues, {recordTypeId: this.rtId,fieldApiName: TYPE_FIELD})     picklistValues;   Then it throws an internal server error. Anybody have an idea as to how I could retrieve the record type Id and then call to get the pick list values like the documentation suggests?  FYI my imports are:  import { LightningElement, wire, track } from 'lwc'; import { getPicklistValues, getObjectInfo } from 'lightning/uiObjectInfoApi'; import TYPE_FIELD from '@salesforce/schema/Account.Type'; import ACCOUNT_OBJECT from '@salesforce/schema/Account'; Value too great for base (error token is "09") Words with different meanings in American and British English This is similar to , but not quite the same.  There are quite a few words which have totally different meanings in American and British English and which are likely to cause confusion when heard by non-local speakers.  What are they?  We are looking for the same word with different meanings (for example jumper), and not words which are different between the two dialects (for example truck and lorry). I want to upgrade the hard drive in my 2012 Macbook Pro to an SSD. I have the parts, but had a question about how to clone the contents of my current drive so I can install it onto the SSD.  I've seen tutorials where people suggest connecting the new SSD to the Macbook prior to installation and using a Carbon Copy Cloner to clone the drive, and then installing the SSD drive.  My question is, can I do a Time Machine backup of my current hard drive on an external hard drive, install the SSD, and then use the Time Machine backup from the external to transfer it onto the newly installed SSD? Is this the same as using the clone program above? I am trying to make a histogram with the fitted curve plotted on it. Here's the mwe:   \documentclass[a4paper]{scrartcl}     \usepackage{tikz}     \usepackage{pgfplots,pgfplotstable}     \usepackage{filecontents}     \pgfplotsset{compat=1.10}     \usepackage[active,tightpage]{preview}     \setlength\PreviewBorder{2pt}     \newcommand{\plots}{0.611201}     \newcommand{\plotm}{2.19882}     \begin{filecontents}{data.dat}     2 0.0629921259843     3 0.0236220472441     4 0.0314960629921     5 0.125984251969     6 0.0629921259843     7 0.102362204724     8 0.110236220472     9 0.0551181102362     10 0.0629921259843     11 0.0314960629921     12 0.0236220472441     13 0.0314960629921     14 0.0629921259843     15 0.0551181102362     16 0.0393700787402     17 0.0472440944882     18 0.00787401574803     19 0.0393700787402     24 0.00787401574803     27 0.00787401574803     33 0.00787401574803     \end{filecontents}     \begin{document}     \begin{preview}      \begin{tikzpicture}     \begin{axis}[     yticklabel style={/pgf/number format/fixed},     scaled y ticks = false,     minor y tick num={1},     xtick pos=left,     legend cell align = left,     legend style={draw=none},     xlabel = {group size},     ylabel = {ratio}     ]     \addplot[blue,ybar,fill, fill opacity=0.3, bar width = 0.8,] table {data.dat};     \addplot[red, line width = 1,domain=1:40,samples=100] {1/(x*sqrt(2*pi)*\plots)*exp(-(ln(x)-\plotm)^2/(2*\plots^2))};     \legend{empirical,lognormal fit}     \end{axis}     \end{tikzpicture}     \end{preview}     \end{document}     As you can see, the legend is not really good. How can I change the legend so it looks more like this? What are good methodologies for creating sprocs that reduce the pain of debugging? And what tools are out there for debugging stored procedures?  Perhaps most importantly, what are indications to look out for that errors are happening in a sproc and not in the code? I hope I'm not all over the board too terribly bad here. Votes for answers to any of the above. Thanks.  For what it's worth, I work in a .NET environment, SQL servers. I try to unzip a zip file, but got an error:  $ unzip COCR2_100.zip  Archive:  COCR2_100.zip   End-of-central-directory signature not found.  Either this file is not   a zipfile, or it constitutes one disk of a multi-part archive.  In the   latter case the central directory and zipfile comment will be found on   the last disk(s) of this archive. note:  COCR2_100.zip may be a plain executable, not an archive unzip:  cannot find zipfile directory in one of COCR2_100.zip or         COCR2_100.zip.zip, and cannot find COCR2_100.zip.ZIP, period.   I googled but didn't find a solution. I was wondering why it is and how I should fix it? Thanks!  The zip file can be downloaded from . It is an application, and here is its website .  My OS is 10.10. System.Windows.Threading.Dispatcher and WinForms? Every time I read the tips for installing an SDK, IDE, some extension and so on, it says, that I should unpack them in /opt folder. Why do I need to do that?   When I was installing Ubuntu, I read that I should set only 10-20 GiB for the / file system and remaining space set for /home. So should I extend the space for root folder, or leave all stuff at /home? Is there any difference? Does the universe have a center? Can I fly back to Italy if my Italian residency card has expired and is being renewed? Can airlines deny boarding if my port of entry is different than the country which issued the Schengen visa? Few days back I did a Europe tour from India. As stated by many (I haven't confirmed official documents), I can apply for a visa from the country which is either my first port of entry in this case Paris or the longest stay which in this case was Italy.  Now following is what happened with me.   My flight was New Delhi to Paris via Istanbul with Turkish Airlines I Traveled from New Delhi to Istanbul (no problem here). When I was boarding to flight Istanbul to Paris, zhe airlines officials (the ones who checks the boarding pass before boarding the flight) told me that I could not board the flight because my visa was issued by Italy and I need to go to Italy First. They were denying the longest stay option of the visa. Moreover NONE of the staff of Istanbul airport were able to understand English so I had to go to a lot of problems before I managed to get tickets to Venice. I somehow managed to fly to Venice from Istanbul after almost 24 hours of struggle at Istanbul airport (without food and water).   So, my question is do the airlines staff have a right to deny flight boarding in this case? Dynamic date range query I'm trying to create two cells that will update my query: A >= date"A1" and A &lt;= date "B1".  My goal is to create a search page for the data, where the end user could insert a date or the =today() function and it would update the query. I am currently getting a formula parse error from:  =QUERY(Data!6:1397,"SELECT A,B,C,D,E,F,G,H,I,J,K,L WHERE A &gt;= date"A1"and  A &lt;= date"B1"") Compute Galois group of $\mathbb F_q/\mathbb F_p$ I have to compute Galois group of $\mathbb F_q/\mathbb F_p$ where $q=p^n$. I know already that $\mathbb F_q/\mathbb F_p$ is galois, so I don't need to prove it. Moreover, I know that \begin{align*}\sigma :\mathbb F_q&amp;\longrightarrow \mathbb F_q\\ x&amp;\longmapsto x^p\end{align*} is an automorphism that fix elements of $\mathbb F_p$ and thus $\sigma \in Gal(\mathbb F_q/\mathbb F_p)$.  Now, I know that if $k&lt;p^n$ then $\sigma ^k(x)=(x^{p})^k=x^{pk}\neq 1$ and thus $\sigma $ is of order $p^n$. Now if I can prove that $|Gal(\mathbb F_q/\mathbb F_p)|=p^n$, then $Gal(\mathbb F_q/\mathbb F_p)=\left&lt;\sigma \right&gt;$ and it would be finish, but I can't prove it since even $X^q-X$ split over $\mathbb F_q$, theis polynomial is not irreducible, and thus, I can't conclude. So how can I find an irreducible polynomial of degree $q$ that split over $\mathbb F_q$ ?