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In Problems in Mathematical Analysis, Volume 2 by Kaczor and Nowak, Problem 2.3.34 is stated as follow.   Find this limit using L`Hôpital rule  $$\lim\limits_{x\to\infty}x((1+\frac{1}{x})^x-e).$$  I have tried by using L'Hospital rule five times but have no result.  I can compute this limit by using Taylor expansion. Rotating an object continously with OnMouseDown I have a script that works but it does not do what I want it to do. My script makes an object rotate on when another is clicked. However, I want the object to continuously rotate until I click on the other object again. Right now when I click it rotates just a bit and stops.  Here is my script:   public class Rotate : MonoBehaviour {     public float speed =50f;     public GameObject target;      public void OnMouseDown(){        target.transform.Rotate (new Vector3(0, Time.deltaTime, 0) * speed);     }  }   How can I make the object rotate continuously until I click it again? Why am I getting shopping trolley notifications about local store savings? I am getting "Shopping Trolley" notifications appearing regularly. The notification looks like this:   The notification is about "Store savings" at a local supermarket and that is it!   Is this notification from Google Maps or another application like Google Assistant? I'm struggling to find the specific setting to disable the notification.  I am also interested to know if this notification could in any way be targeted advertising generated by the store. My marketing preferences with the store are opt-out and this strikes me as very dumb advertising. Surely Google isn't doing this? Is there a means that a store can generate notifications like this? Could it be targeted if they have my email address?  These are pain and I want to understand why they are spamming me and disable them without disabling everything else.  I can see various options under Google Maps, settings, notifications. Which setting would apply? Could it be "New on maps, Get occasional updates about new features in your area"? I can't see what setting to suppress!  Thanks for all help. Command substitution: splitting on newline but not space I know I can solve this problem several ways, but I'm wondering if there is a way to do it using only bash built-ins, and if not, what is the most efficient way to do it.  I have a file with contents like  AAA B C DDD FOO BAR   by which I only mean it has several lines and each line may or may not have spaces.  I want to run a command like  cmd AAA "B C DDD" "FOO BAR"   If I use cmd $(&lt; file) I get  cmd AAA B C DDD FOO BAR   and if I use cmd "$(&lt; file)" I get  cmd "AAA B C DDD FOO BAR"   How do I get each line treated a exactly one parameter? Proof that $n^2 < 2^n$ How do I prove the following statement by induction?  $$n^2 \lt 2^n$$  $P(n)$ is the statement $n^2 \lt 2^n$  Claim: For all $n \gt k$, where $k$ is any integer, $P(n)$  (since $k$ is any integer, I assume I have to prove this for positive and negative integers)  So let base case be $P(1)$, and I have to prove $P(n)$ for $n \ge 1$ and $n \lt 1$  $P(1)$ is $1^2 \lt 2^1$ which is clearly true.  Induction hypothesis: $k^2 \lt 2^k$  Inductive step $(k+1)^2 \lt 2^{(k+1)}$  $(k+1)^2 = k^2 + 2k + 1$  $k^2 + 2k + 1 \lt 2^k + 2k + 1$ by inductive hypothesis  Not sure how to proceed. Is my previous intuition that I have to prove this for $n \ge 1$ and $n \lt 1$ correct? YA novel where clumsy boy gains wings I'm trying to remember the name of a novel I read as a pre-teen.  If I recall correctly, it would have come out in the 90s (though it may have been a reprint).  The novel is set in modern times.  I recalled this because I've been reading a lot of urban fantasy lately, and this may be the first 'urban fantasy' book I read - our world, but with a touch of magic.  There's a somewhat clumsy, out of shape teenaged (or almost teenaged) boy who doesn't have a father.  His father had been a stage magician who was constantly frustrated by his son's complete inability to preform stage magic, despite a prediction saying he would have a great or powerful magic.  His father had died before the book started, I don't recall how long before.  The boy does something nice for an old woman (I don't recall what) and she gifts him a magical potion.  A drop of it, rubbed on his shoulder blades, will make him grow wings.  The book follows him for the summer, as he spends his evenings flying.  He makes himself a toga-like shirt out of some old curtains and spends time flying around at night.  I recall one scene where he learns about two children out in the middle of the bay (perhaps the book is set in San Fran?  I don't recall) in a rowboat with one oar.  He saves them (by pulling them back to shore using a rope they had with them) and gets mentioned in the paper as an angel.  At the end of the book, the potion has run out.  There's only a tiny little bit left, and when he rubs it in, it creates only a single feather.  Around that point, the boy realizes that he's no longer getting winded going up several flights of stairs and he's gained a lot of self-confidence.  From what I remember of the copy I read, the cover featured a shirtless boy wearing jeans standing in front of a mirror, looking at the large white feathered wings that had grown from his back. "who" vs. "whom" and when to omit the relative pronoun This is the boy who was asked by the teacher to stay back after school. This is the boy whom the teacher asked to stay back after school. This is the boy the teacher asked to stay back after school.   Are the sentences above correct ? How to extend the text under summation symbol without making extra space Refer to an item in `dirs` I use pushd to work with multiple directories in bash and zsh. I've aliased dirs to dirs -v so that I get an ordered list when I want to see what's on the directory stack:  chb$ dirs 0  /Volumes/banister/grosste_daever_gh/2013-03-27/reader 1  /tmp/20130618202713/Library/Internet Plug-Ins 2  ~/code/foo/view/static/css 3  ~/Downloads   Is there a way (either in bash or zsh) that I can refer to one of the directories listed on the command line using an alias for its position on the stack? For example, instead of typing:  chb$ cp ~/code/foo/view/static/css/baz.css ~/code/bar/view/static/css/   I'd type:  chb$ cp &lt;2&gt;baz.css ~/code/bar/view/static/css/   ...or something like that, maybe using a dollar sign and a variable name instead of &lt;n&gt;. We roll a six-sided die ten times. What is the probability that the total of all ten rolls is divisible by 6? So the question is really hard I think. I tried using a simple way by calculating the probability of each combination that makes a sum divisible by six, but it would take forever. Does anyone have any ideas?  Suppose that we roll a six-sided die ten times. What is the probability that the total of all ten rolls is divisible by six? How to install Anaconda on Ubuntu? How to install  on Ubuntu?   Is there a way to use apt-get install?   I only have command line access to my server. How do I install Anaconda on Ubuntu 14.04 from the command line? How do you split a long exact sequence into short exact sequences? How does one split up a long exact sequence into short exact sequences?  Say you have some longs exact sequences of modules $$ 0\longrightarrow M_1\stackrel{\phi_1}{\longrightarrow}M_2\stackrel{\phi_2}{\longrightarrow}M_3\stackrel{\phi_3}{\longrightarrow}M_4\stackrel{\phi_4}{\longrightarrow}\cdots $$ I've read it's possible to split this into short exact sequences. What exactly does that mean? Would it be written as short exact sequences, one appended to another like $$ 0\longrightarrow N_1\longrightarrow M_1\longrightarrow N&#39;_1\longrightarrow 0\longrightarrow N_2\longrightarrow M_2\longrightarrow N&#39;_2\longrightarrow 0 \longrightarrow\cdots? $$ If so, how does this work? Merci. why does fdisk add one additional sector when creating partitions? I'm playing around with fdisk and I tried to create a partition on an empty USB drive. Here's how that went: Command (m for help): n Partition number (1-128, default 1): 1 First sector (34-61187102, default 2048): 2048 Last sector, +/-sectors or +/-size{K,M,G,T,P} (2048-61187102, default 61187102): +30000000           Created a new partition 1 of type 'Linux filesystem' and of size 14,3 GiB.  so just one partition with 30 million sectors. However, when I check how many sectors it contains I get:  I'm checking with a different program and I see again that additional sector:  Sorry for the pettiness :) I'm learning. Kernel Panic - not syncing: VFS: Unable to mount root fs on unknown-block(0,0) Upon trying to upgrade from 10.10 to 11.04 all seemed to go well until the restart. This error message is what comes up:  Kernel Panic - not syncing: VFS: Unable to mount root fs on unknown-block(0,0)   How do we fix that? I installed an Ubuntu alpha or beta and have been keeping it up to date.   So, Should I presume that my system has automatically updated to the next alpha or beta, and will be running the official release when it's finished? My question isn't how they receive the energy to jump, but why.  When someone views an element's emission spectrum, we see a line spectrum which proves that they don't exist outside of their orbitals (else we would see a continuous spectrum).  Electrons can be released in the form of beta decay, thus proving that they are capable of traveling outside of orbitals contrary to the statement my teacher said that they stay within orbitals. Then, to add to the confusion, the older model of rings floating around a nucleus has, from what I can tell, been outdated, which would support this model. My teacher's explanation was that the electrons made a quantum jump of some kind. How do electrons move between orbitals or do we know how they jump, excluding the reason that energy causes them to jump, and why are positrons formed sometimes instead of electrons in Beta decay?  When I'm asking "how do electrons jump" I would like to know how an electron can jump between each orbital such as how it moves and how it knows where to jump since it appears to be a jump where the electron doesn't slow into a orbital position. Specifically how they jump what is this Atomic electron transition, I understand that they jump and that they do this through absorbing and releasing energy but what is this Atomic electron transition other than what is already on the wikipedia article . What kind of questions can I expect to see on a qualifying exam? In mathematics, there are certain open questions which are the subject of current research (think of the newest papers in the top journals).  I have also heard that some graduate programs ask questions such as these on their qualifying exam.  How common is this practice?  What kinds of questions can I expect to see on a qualifying exam?  I know that a qualifying exam typically tests the knowledge gained in graduate school, but I'm not sure to what extent this knowledge is tested?  How "advanced" should I expect these questions to be? Profile page "activity" tab is broken Best way to select a subset of items in a long list One of our clients wants us to build a web application to share information about the magazines he publishes. Each edition of a magazine contains a variable amount of advertisers. These advertisers come from a central pool of advertisers. This pool contains (at the moment) about 150 advertisers. Each edition of a magazine contains a subset (about 70-80) of these advertisers.  Our client wants us to come up with a way for him to add 70-80 advertisers from this list of 150 to an edition of a magazine. It needs to be as fast as possible, as easy as possible and as intuitive as possible.  What would be an ideal solution here? I was thinking about something in the lines of the image below.   List of available advertisers. List of selected advertisers. Advertisers have a delete button. Textbox with auto-suggest for advertisers in the list on the left. &lt;Enter> removes the advertiser from the left list and adds it to the right one. Textbox gets cleared and remains focus.   My colleagues suggested drag-and-drop or just one list with a checkbox for each advertiser, but those approaches force the user to do a lot of searching and clicking. With my approach the user can just keep on typing.  Any other suggestions for this situation? I don't understand why the interior of $\mathbb{Q}$ in $\mathbb{R}$ is empty, since, for every ball with the center being a rational number, given an $\epsilon&gt;0$, I can find an infinite sequence of rational numbers that approach this point. For example, take $\frac{1}{2}$. The sequence $\frac{1}{2}+\frac{1}{n}$ can be made as close as I want to the number $\frac{1}{2}$, therefore I can always have open balls with center $\frac{1}{2}$ such that there are rationals inside it.