$f(z)=\frac{1}{z-\sin z}$  Now $z-\sin z=z-(z-\frac {z^3}{3!}+\frac{z^5}{5!}\cdots)$  After solving $z=0$ is a pole of order $3$ for $f(z)$ and $$f(z)=\frac1{z^3(\frac1{3!}-\frac{z^2}{5!}+ \cdots  )}$$ What is next?
$$\frac{1}{z-\sin z}$$ $$\frac{1}{z(1-\frac{\sin z}{z})}$$  the laurent's transform is also used to simplify the function.  the residue is found a $\frac{2*36*2}{5}$ but the actual answer is given as $\frac{3}{10}$ the residue is given as The solution is incorrect and also the pole is of the order 3.
How to undelete notes on iPhone "Notes" app? iPhone has a default "Notes" app which allows us to store notes. Stored notes can be deleted by hitting the "Delete Note" button:    How do we recover a note that is accidentally deleted?  Is there anyway to undo the delete? One of the mysteries that my numerics class left me with are "stiff systems". Our prof didn't really manage to explain what they are. Now that the class (and the test) are over, I'm still curious.   The most concise definition about "stiff systems" I've found so far is: "There is no universally accepted definition of stiffness". So, if there is none, I don't expect one.   I'd be thankful about information on both of the following points:   From what kind of (real-world) problems do stiff systems arise? What's so "stiff" about them? What's the good thing - or the bad thing - that I'd worry about when I have to numerically solve such a real-world problem? How to find all the available tools in mac terminal? I am trying to setup a bunch of development projects in my Mac. I have to run various tools like python, ruby, scala, groovy etc.  To see if a tool is available I use options like   ruby --version.    Instead I would like to see all the list of tools available in Mac terminal via a single command. What is the command/options for it? Display each sub-directory size in a list format using one line command in Bash? I want to get a list of the directories and their sizes in a list format like how you get when you do a ls -l.  The thing is that is there a one line command that can do this? I see others have long commands just to output this. That's just too long.  What command can do this or combination of commands that can be easily typed? du -h gives it, but it displays all of the sub-folders which is not what I want. just the current directories folders. Ubuntu 16.04 hangs on splash screen during boot What happens when you target a "magical effect" with Dispel Magic? You can’t buy your kids clever. What’s more, if they’re merely above average, by sending them to some hideous Holland Park hothouse, you’re probably buying them miserable.  — Alex Proud,   ""   As far as I know, clever and miserable are both adjectives, not nouns. So why were they used with to buy? Is this an idiomatic way of saying You can't buy your kids intelligence and you're probably buying them (moral) misery? If so, what is the idiom used here? I'm not familiar with it. QGIS Graphics Glitch after changing CRS Thus is a picture of both of my hard-drives:    My C Drive and my D drive. I want to put Ubuntu onto my D Drive. Now my question here is if i do install onto my D Drive then how should I do it in order to retain use of the drive. I intend to partition about 60 gigs from it. Now after doing that I should still have about 830 gigs left. I want to still be able to use that in Windows. So how and will I be able to retain use of the drive after Installing? I have installed once before and I believe i did it wrong because not only could Windows not recognize my D drive but I also lost all the data on it.   My computer is a Lenovo Y700 It is a UEFI (I believe i got that right). Are aerosol cans allowed and safe, in checked luggage? subequations and array in braces Why are my Cycles settings missing? so I'm working on a little bathroom scene and wanted to make a clay render. I started looking for the material override which I kinda knew where it was and on the way I switched my render engine accidently to workbench instead of cycles. Switched to cycles all my seetings on the render tab are missing except color management and free style. Hows that? I restarted blender multiple times and tried some other stuff but nothing changed a thing, and I'd rather avoid a new installation Re-mounting an un-mounted USB stick Why does my minecraft server disconnect the internet when it crashes? How to pluralize an acronym which ends in 'S' correctly? When using the acronym package, how can you  an acronym which ends on 'S'?  Take the acronym: OS - operating system  It should be pluralized as OS's, but is pluralized as OSs when using \acp. Why can't you get awarded the bounty for answering your own question? Consider this question on .  I put out a 200 bounty on the question, but did not get an answer from anyone other than myself that worked.    In fact, my answer is also the highest up-voted on it at this point.  I know that allowing OP's to retract a bounty can be a slippery slope; in fact I think that once the bounty is put up it should stay up.  But why not allow the OP to answer their own questions with a bounty and reward it to them if they receive the same up-votes as others?  Yes, I am fully aware that bounties are a risk.  People will use them for numerous reasons such as trying to draw extra attention to their issues.  However, in my specific question, the only valid answer is the one that I gave.  Had it been anyone else's question, I would have received the bounty, but since it was my own I did not. How to edit 'etc/hosts' file in non-rooted phone? I'm using LineageOS 14.1 and don't want nor need to root it. How can I remount /system rw and edit /system/etc/hosts?  All answers in "" expect a rooted phone. Some questions are getting closed as duplicates - good, the system is working. Unfortunately, some are getting closed as duplicates of other questions which are already deleted. This leaves all 1-9,999 reputation users left scratching their heads when they try to view the duplicate. Even worse, imagine being the author of the question and having your question closed as a duplicate when the original question isn't accessible.  I think something is wrong. Today I undeleted a question (left it closed) since it was referenced in the close-reason for another question. Comments indicated that people were clearly irritated that they could not access the duplicate     [Comment] Ok, who thought it was a good idea to close this as duplicate of a deleted question, which most people cannot even see? For the record, I'm reopening - clearly there's enough interest in this question. – Kobi 14 hours ago   ---   [Comment] The PosibleDuplicate link is broken. Voting to reopen. – Rahul G 7 hours ago   ---   [Flag] Closed as duplicate of a deleted question, fail. Thanks for moderating. – {username removed} 14 hours ago   My undelete-action was short-lived, as a few users returned to delete the post again.  It certainly cannot be desirable to reference posts that the vast majority of users cannot even see, especially when the author of the redundant question cannot see (at the time of writing this, the author has a reputation of 18).  I'm not sure what the solution is to this, but I'd like to hear some ideas.  Questions  Question:  Duplicate of: Can [sic] be used to highlight a punctuational error?    In the sentence below, the bracketed sic would obviously denote that the punctuation preceding it was an error &mdash; that is, a semicolon should supplant the comma. Has anybody ever seen this usage, and would you support it?     The sun is high, [sic] put on some sunblock. How to cite lecture notes? (and should I even do this?)