There is a function       $f(x):= \begin{cases} e^{-1/x^2}, &amp; \text{if $x \neq 0$} \\ 0, &amp; \text{if $x=0$} \end{cases} $.     That function's $n$-th derivative is $0$ : $f^{(n)}(0) = 0$. How to derive that?
Given the function   $$ f(x) = \left\{\begin{array}{cc} e^{- \frac{1}{x^2}} &amp; x \neq 0 \\ 0 &amp; x = 0 \end{array}\right. $$  show that $\forall_{n\in \Bbb N} f^{(n)}(0) = 0$.  So I have to show that nth derivative is always equal to zero $0$. Now I guess that it is about finding some dependencies between the previous and next differential but I have yet to notice one. Could you be so kind to help me with that?  Thanks in advance!
Why do gases have weight? I know that a gas is made of atoms or molecules moving freely in space.  When these particles hit the walls of where they're kept in they cause something called pressure.  But these particles never pile up on each other and push a surface down by their weight so that we can measure it as weight, not pressure.  So why do gases have weight? How to add Lat/long columns to a point layer which is not in WGS84? I need to extract the Lat/long coordinates of the centroids of districts. My QGIS project SCR and the different layers have all been set on "WGS 84 / UTM zone 18N".   I've created the centroids using the usual tool. I could then extracted the coordinates using the "Vector > Geometry Tools > Export/Add Geometry Columns", or saving the layer in CSV typing "GEOMETRY=AS_XY" in the "Layers" part of the "OGR creation options".  Nevertheless, both methods output Cartesian coordinates, whereas I need Lat/long coordinates. What is the "correct" way of embedding text into math mode? Lets say I have something like:   \[ Let x = number of cats \]   (This is a contrived example, but pretend we are actually inside a long align environment block...) "Let" and "number of cats" need to be written like normal text, while x= needs to be math type text.  I've seen this:  \[ \mbox{Let } x = \mbox{ number of cats} \]   and this:  \[ \textrm{Let } x = \textrm{ number of cats} \]   They seem to produce equivalent output, but I'm not sure which is the "correct" one. Also, they are not ideal in that the extra space needs to be placed inside the text mode block, otherwise it is ignored as math mode and butts the text right up against the math.  Ideally there would be some command which allowed embedding text into an equation, which correctly inserted leading and trailing space around the block as required without adding space inside the text block.  How does one do that "correctly"? Is this sentence grammatically correct?  Anyone who loves the English language should have a copy of this book in their bookcase.  or should it be:  Anyone who loves the English language should have a copy of this book in his or her bookcase. I have a site that is in French and English. I am able to successfully setup so that users can switch back and forth between the two domains to view either language, however I cannot seem to keep users logged in. When they are logged into the english domain and then switch to the french domain they are required to login again. However if they switch back to the english domain they are still logged in.  As an example we'll use www.english-domain.com as the base (default) domain and www.french-domain.com as the secondary domain  In settings.php I have modified the following, however it doesn't seem to be keeping them logged in. Am I missing something?  /**  * Drupal automatically generates a unique session cookie name for each site  * based on its full domain name. If you have multiple domains pointing at the  * same Drupal site, you can either redirect them all to a single domain (see  * comment in .htaccess), or uncomment the line below and specify their shared  * base domain. Doing so assures that users remain logged in as they cross  * between your various domains.  */ $cookie_domain = 'english-domain.com';   Note: That I have also flushed both site and browser cache as well as deleted any cookies left on my machine.  Update:  Here are my language settings: Is there the easiest way to toggle (show/hide) navigational grids in TikZ? In PSTricks, we can toggle the grids easily by showgrid=[false/true]. How to do it in TikZ? Doing as follows is tedious.    \documentclass{minimal} \usepackage{tikz}  \begin{document}   \tikzpicture  \draw[gray,very thin] (-4,-2) grid (4,2); \foreach \x in {-4,...,4}   \draw[red] (\x,-1.9) -- (\x,-2.1) node [below] {\x};   \foreach \y in {-2,...,2}   \draw[red] (-3.9,\y) -- (-4.1,\y) node [right] {\y};  \draw (0,0) circle (2);   \endtikzpicture    \end{document}   Is there the easiest way to toggle (show/hide) navigational grids in TikZ?  Edit  The navigation needs not only the grids but also the labeling numbers. How to prevent automatic redirection of 404 errors and "incorrect" URLs? Wordpress has a feature whereby it will automatically redirect your URLs if it percieves them to be written wrongly. Here is an example: I have a page called my-page  If I go to:  www.mysite.com/something/my-page/   it will immediately redirect me to   www.mysite.com/my-page/   as nothing exists at the first URL.   How can I turn this feature off, and instead just get a 404 if incorrect URL's are typed in? Markdown in chat fails for multi-line messages How to create a new figure in MATLAB? How long do you get to use a UK standard visitor visa from time of issue or is it valid for entry indefinite I am going to apply for a standard visitor visa for my girlfriend to enter UK. If it is issued how soon does it have to be used after issue, ie. validity until time of entry? In wikipedia FKT algorithm is given for planar graphs. Not anything for complete graphs. I need to find the number of perfect matchings in complete graph of six vertices. A local IP address (RFC 1918) on my network that is not … local I've noticed an IP address today on my network (192.168.15.1) which when visited actually goes to a page that has a router webconfig page (Not my router)  The puzzling thing is that i tried traceroute 192.168.15.1 which said that the distance between me and that host is 9 hops, whereas the distance between me and any other computer on my home network is 2 hops away (My computer --> Router --> Host)   Can someone please explain what's going on here ?  tracert output:  Tracing route to 192.168.15.1 over a maximum of 30 hops    1    &lt;1 ms    &lt;1 ms    &lt;1 ms  192.168.1.1   2    47 ms    51 ms    49 ms  [163.121.171.123]   3     *        *        *     Request timed out.   4   128 ms     *        *     163.121.211.134.dnet.net [163.121.211.134 ]   5     *      134 ms   126 ms  10.37.242.18   6    94 ms    90 ms    95 ms  10.35.2.157   7   178 ms   254 ms   206 ms  10.32.8.107   8    85 ms    57 ms   318 ms  10.35.0.186   9   215 ms   241 ms   230 ms  192.168.15.1  Trace complete. I am using QGIS 2.6.1 and have worked in an Excel file database (which was actually converted from a Shapefile). I have managed to convert it as CSV file and load it into QGIS (displays data fine) but I have trouble to convert it to a shapefile.  I can view it but I can´t add or alter data in this file. I think I have to save it as a database.   Any clues how to convert the xlsl-data to a database and finally to a shapefile? Installing node with apt-get or downloading the Linux Binaries (.tar.gz) What is the difference between installing node.js with 'sudo apt-get install nodejs' or downloading the Linux Binaries (.tar.gz) and following  instructions?  Is the outcome the same? Bad Eyesight and Evolution Why do many humans have bad eyesight, such as near-sightedness, which hampers performance in a wide variety of tasks? Shouldn't there be evolutionary pressure towards better eyesight? Why is the subject omitted in sentences like "Thought you'd never ask"? "Thought you'd never ask" is "I thought you'd never ask" with "I" omitted. "Hope this helps" is "I hope this helps" with "I" omitted.   In English grammar, normally every sentence should have a subject, right?   My first thought is that these two examples are so often used that they are like set phrases. But these are not really set phrases. You can alter the words after "thought" and "hope".  Another possible explanation is the tendency to drop the subject if it is the first person pronoun. It seems that in many languages, such as Spanish, Italian and Japanese, the first person subject is usually omitted. Maybe English is going the same way? (Not exactly the same, since in Italian, verb forms change according to the person, so the subject is not necessary to understand who one's referring to.)  And, apparently, such omission is more common in spoken English than in written English.  Are there more examples of such first person subject omission? How frequent is it? Which wire is negative on this PC fan? I just got this PC fan and it has a 3 pin connector, I know the wire with the white stripe is positive but how can I find out which of the other two wires are negative?  If you can't see the photo, here is a link to it: Make Bash autocomplete guess the closest approximation I have a somewhat uncomfortable keyboard on my laptop, resulting in that I sometimes misspell things in Bash and when pressing Tab for an auto-completion nothing happens.   Is it possible to have Bash guess what I meant to type, by for example when wanting to change directory to Documents and then mistyping cd ocum[TAB], given no other folder beginning with "ocum" is present, Bash interprets it as cd Documents/ since it is the closest possible action to do?   Or is this idea terribly complicated to achieve? Process management and high technology weapon. Novel name and author? I am looking for help to point me out at a very old novel (likely from the '60s) about two empires at interstellar war. When it comes to starships, one is technologically very advanced, and the other has very low and inefficient technology.  The highly advanced empire has apparently strong chances to win the war, in particular considering a new technology they were developing. I remember the technology to work like this: consider the space as a flat surface, and on this surface, a disk around the spaceship. When the technology was turned on, this disk was stretched out, as made of rubber, so that it produced a cone, with the tip being the spaceship. The spaceship was therefore teleported 10 parsec away (if I remember correctly), but retained all the connections to the original position. If the spaceship moved, the cone moved as well. This allowed to move in position among enemy ships completely unnoticed, by stretching while afar, then moving in the proper position 10 parsecs away, then destretching.  Despite this technology, the empire lost the war because of delays. It's a perfect example of how having a disruptive technology does not guarantee to win against the competitors.  I am trying to find out the author and name of this novel, hopefully with the date of publication and in which journal/magazine. I've found some code that could add a modifier but none can set parameters like Octree.