Evaluate:     $$\lim_{x\to 0} \sin (\dfrac {1}{x})$$   My Attempt:  let $$\dfrac {1}{x}=k$$ As $\dfrac {1}{x}\to 0$, $k\to \infty$ Now, $$=\lim_{k\to \infty} \sin k$$
show that $$\lim_{n\to \infty}\sin{(n^m)}$$  divergent,where $m\in N^{+}$  I have kown $$\lim_{n\to\infty}\sin{n^2}$$  to be divergent and dense in $[-1,1]$. This is very  famous problem,the problem is first is post $AMM$( The American Mathematical Monthly,1970-1975) problem,and after some years  $AMM$ post $\sin{(n^{14})}$ in $[-1,1]$ was dense? and this is open problem.so I Guess  $$\sin{(n^m)}$$ is dense in $[-1,1]$.
I would like to install the restricted extras package, which I didn't select during the install. How can I do that?        is a meta-package that installs:         Support for MP3 and unencrypted DVD playback   Microsoft TrueType core fonts   Flash plugin   codecs for common audio and video files How to capture Control+D signal? If $H \leq G$ and $[G:H]! \leq |G|$ then $G$ is not simple Seeking QGIS tutorials and web resources? Remove HTML tags from a String How to sample a function non-uniformly? See this example code:  \documentclass{article}  \usepackage{pgfplots} \pgfplotsset{compat=1.10} \begin{document}   \begin{tikzpicture}     \begin{axis}[                  xmin=-0.1,                  xmax=1.1,                  ymin=-1.1,                  ymax=1.1,                  domain=0:1,                  samples=30                 ]       \addplot[blue] {sqrt(x)};       \addplot[purple] {-sqrt(x)};     \end{axis}   \end{tikzpicture} \end{document}   The result appears acceptable far from zero, but near zero it's too much undersampled:    Increasing samples value makes the plot nice, but it considerably slows down processing. As a workaround I could just plot the inverse in a parametric plot (i.e. (y^2,y)), but in my actual code it'd require quite a bit of additional work.  Is there a way to provide a custom sampling function or specify different density of samples in different parts of the domain? Moving a very large (40 TB) DB from a 2008 server to a 2016 server Moving from HTTP to HTTPS in Google Search Console I'm moving from HTTP to HTTPS for my entire site. The site is currently added to Google Search Console (formerly Google Webmaster Tools) as www.example.com and all the pages are indexed without using SSL.  How do I go about moving to the new HTTPS URLs on Google Search Console?   Do I just submit an updated sitemap which has the HTTPS URLs or do I add a new site as https://www.example.com and submit the sitemap with HTTPS URLs? All current URLs are set to redirect to their HTTPS counterparts. Do I add multiple properties to Google Search Console? "implements Runnable" vs "extends Thread" in Java From what time I've spent with threads in Java, I've found these two ways to write threads:  With implements Runnable:  public class MyRunnable implements Runnable {     public void run() {         //Code     } } //Started with a "new Thread(new MyRunnable()).start()" call   Or, with extends Thread:  public class MyThread extends Thread {     public MyThread() {         super("MyThread");     }     public void run() {         //Code     } } //Started with a "new MyThread().start()" call   Is there any significant difference in these two blocks of code ? I'm new to linux and the terminal. As I learn how to use the terminal to navigate through directories, I like to use the gui file explorer to mirror my terminal navigation. The icons and file extension info in the gui file explorer help me figure out what everything is. However, I can't access the root folder via the gui, I can only access it via the terminal. Is there a way to enable access to the root folder outside of the terminal? My prisoners wont move from the holding to cell to the actual cell I have a cell block with 25 cells but none of my prisoners will move there from the holding cell. I have working power and water beds and toilets they are separate from each other it has all the requirements why wont it work? Any ideas? This is a question thats been bothering me a while. I don't even know if it makes sense or not (like if it is a physics question or becoming a philosophical one). But here it goes. The crux of my question basically is that we all know that we can't see light (like in its photon or electromagnetic wave form) directly when it is traveling past us. However, we also know that the way we see objects is by light reflecting off them. This then means that we are "seeing" the light reflecting from the object which then sends the signal to our brain saying that we are seeing a particular object. We know that both light traveling past us and light reflected from objects are made of photons (so they are the same kind)? So then my question is that what is happening to the photon of a light after it is reflected from the objects, that causes us to see it or the object, but on the other hand we can't see light as it is directly traveling past us. Link2SD not working completely Function returns None without return statement So, according to Einstein's theory of general relativity, gravity is not a force instead it is a consequence of objects with mass deforming spacetime, right? And so, according to him, there is no difference between standing on a platform accelerating upwards at 9.81 m/s^2 and standing on Earth, right? But, there is a difference. At least, I think it's a valid difference. If you drop two apples from a high altitude on Earth, not only will they accelerate downwards at 9.81m/s^2 but they will also slightly move towards each other because the Earth is a sphere and gravity acts radially inwards pulling the two apples closer to each other. But if you drop the apples from the same height above the accelerating platform, the apples will only appear to accelerate downwards at 9.81 m/s^2 but will not move towards each other like they would on Earth. Why is this true? Is this even a valid difference? If it isn't, why isn't it? How to load a taxonomy term with case-sensitive? I used this      $this-&gt;termStorage-&gt;loadByProperties(['name' =&gt; 'test']);   I got two terms: Test, test. I want to get only one: test  This is working without case-sensitive:       $this-&gt;termStorage-&gt;getQuery()-&gt;condition('name', 'test', '=')-&gt;execute();       \Drupal::database()-&gt;select('taxonomy_term_field_data', 't')       -&gt;condition('t.name', 'test')       -&gt;fields('t', ['name'])       -&gt;execute()       -&gt;fetchAll();       \Drupal::database()-&gt;query("SELECT name FROM taxonomy_term_field_data WHERE name='test'")-&gt;fetchAll(); how to calculate $$\int_0^\infty \frac{x^{3}}{e^{x}-1} \; dx$$   Be $q:= e^{z}-1 , p:= z^{3}$ , then $e^{z} = 1 $ if $z= 2\pi n i $, so the residue at 0 is : $$\frac{p(z_{0})}{q&#39;(z_{0})} = 2\pi i n ^{3}$$  problem is that this is not symmetric, so how does one find the definite integral? Introduce a  "general reference" close reason There is a certain amount of questions that are absolutely trivial in nature: How to format a date, how to concatenate a string, et cetera. Questions that could be solved by taking a look into the manual.  Random examples from the tags I frequent:                What those OPs need is a link to the right manual, which we should give them. But the question serves no purpose. They don't even have a use by being searchable,  because any sane search query would lead to the actual manual as the first hit.  Jeff discusses the possibility of introducing a new close reason for this over at  According to Robert's suggestion there, it could go like this:     general reference: this question is too basic; the answer is indexed in any number of general internet reference sources designed specifically to find that type of information.   Please please implement this.  Add a field (like the "enter duplicate ID here" popup) for users to suggest the correct manual link:    The suggested links would then be shown in a block in the top section of the question, like duplicate links.   Also, the amount of reputation earnable from these trivial questions is appalling. I'm sure a great portion of most high-rep users' points (including mine) is from answering "what was that function for replacing a string again?" type questions. This dilutes the value of reputation as a measure of true expertise a great deal.  I would suggest that answers to questions that get closed as "general reference" are made community wiki retroactively, taking away any reputation earned. Trying to format USB (using Linux/fdisk) so it shows up on my Mac I have a USB drive that I can see/access/modify/etc in Linux/Ubuntu but it doesn't show up on my Mac OSX.  I did sudo fdisk /dev/sdb (where my USB is) and then g to create a new GPT partition table, n to make a new partition, used all default settings, then w to save and exit.  Then I did sudo mkfs.fat -F32 /dev/sdb1 to format the partition with a FAT32 filesystem.  I ejected the USB and put it in my Mac and it doesn't show up / get detected.  What did I miss? In my Master thesis, I used this:  \begin{itemize}[label=\ding{167}] \item Access Windows XM from Ubuntu Server \item List the directories contents of Windows XP \end{itemize}   The output is:  My question: must I avoid the use of  such beautiful things when writing my thesis or is it a normal thing to do ?