Taylor series of $\ln\frac{1+x}{1-x}$
Taylor Expansion $\log(\frac{1+z}{1-z})$
Are there irreducible polynomials that are partially solvable by radicals? In general, polynomials of degree 5 or higher, with rational coefficients, are not solvable by radicals. There are some exceptions and trivial cases, for example $x^5-5x+12$ and $x^{100}+x^{25}+3$, respectively.  All irreducible polynomials with rational coefficients, that I am aware of, have either none or all roots that can be expressed by radicals.  Do partially-solvable irreducible polynomials exist? If they do, are there any examples known?  I mean, for example, an irreducible polynomial of $n$th degree that can be split over $Q(\sqrt{2})$ into two polynomials of 3rd and $(n-3)$th degrees, where the polynomial of $(n-3)$th is not solvable by radicals.    At  Alexander Gruber wrote:     Polynomials which are not solvable by radicals have (at least one) root that cannot be written by any combination of the operations of addition, multiplication, and the taking of nth roots.   I am not sure if he meant only reducible polynomials, and/or with non-rational coefficients, as polynomials that have "at least one" root that cannot be expressed by radicals. sudo -k vs. sudo -K I know what the man page has to say about the -K and -k :     ‑K       The ‑K (sure kill) option is like ‑k except that it removes the user's   cached credentials entirely and may not be used in conjunction with a   command or other option. This option does not require a password. Not   all security policies support credential caching.      ‑k[command]       When used alone, the ‑k (kill) option to sudo invalidates the user's   cached credentials. The next time sudo is run a password will be   required. This option does not require a password and was added to   allow a user to revoke sudo permissions from a .logout file. Not all   security policies support credential caching. When used in conjunction   with a command or an option that may require a password, the ‑k option   will cause sudo to ignore the user's cached credentials. As a result,   sudo will prompt for a password (if one is required by the security   policy) and will not update the user's cached credentials.   So if there is no need to use a command in conjunction with these options, am i correct in assuming K is always the better option to use rather that k? In what order should one apply max HP reduction and damage? A character at 10/26 HP is hit by a Wraith and fails the Constitution saving throw. They take 21 damage and their maximum HP is reduced to 5.  Are they unconscious because the 11 excess damage is less than 26 or dead because it's greater than 5? I tried Office 2013, but now wish to uninstall it. I tried to uninstall it but it always hangs at step  2 out of 4. It uses no CPU and no disk activity. So basically it's just idle.   Does anyone have a solution to this problem? How to enable or disable services? I read about how to enable and disable services in Ubuntu and it seems that there are different possibilities to manage them.  The first method I found is update-rc.d to add new services to startup, which aims on the /etc/init.d folder and its contents.  The other one I found is to edit .conf files in the /etc/init folder.  What's the recommended way to enable / disable / add services and why?  Could you please give a short bulletproof step by step example on how to add a service in Ubuntu and enable and disable it? Proper submodules of Noetherian modules are intersections of indecomposable modules If $M$ is Noetherian, any submodule $N \neq M$ can be written as a finite intersection of intersection-indecomposable ones.   I just don't know how to begin with the proof of this proposition.   Very kind of you for reading or answering. I have a query pattern that must be very common, but I don't know how to write an efficient query for it.  I want to look up the rows of a table that correspond to "the most recent date not after" the rows of another table.  I have a table, inventory say, which represents the inventory I hold on a certain day.  date       | good | quantity ------------------------------ 2013-08-09 | egg  | 5 2013-08-09 | pear | 7 2013-08-02 | egg  | 1 2013-08-02 | pear | 2   and a table, "price" say, which holds the price of a good on a given day  date       | good | price -------------------------- 2013-08-07 | egg  | 120 2013-08-06 | pear | 200 2013-08-01 | egg  | 110 2013-07-30 | pear | 220   How can I efficiently get the "most recent" price for each row of the inventory table, i.e.  date       | pricing date | good | quantity | price ---------------------------------------------------- 2013-08-09 | 2013-08-07   | egg  | 5        | 120 2013-08-09 | 2013-08-06   | pear | 7        | 200 2013-08-02 | 2013-08-01   | egg  | 1        | 110 2013-08-02 | 2013-07-30   | pear | 2        | 220   I know one way of doing this:  select inventory.date, max(price.date) as pricing_date, good from inventory, price where inventory.date &gt;= price.date and inventory.good = price.good group by inventory.date, good   and then join this query again to inventory. For large tables even doing the first query (without joining again to inventory) is very slow.  However, the same problem is quickly solved if I simply use my programming language to issue one max(price.date) ... where price.date &lt;= date_of_interest ... order by price.date desc limit 1 query for each date_of_interest from the inventory table, so I know there is no computational impediment.  I would, however, prefer to solve the whole problem with a single SQL query, because it would allow me to do further SQL processing on the result of the query.  Is there a standard way to do this efficiently? It feels like it must come up often and that there should be a way to write a fast query for it.  I'm using Postgres, but an SQL-generic answer would be appreciated. Catch multiple exceptions at once? It is discouraged to simply catch System.Exception. Instead, only the &quot;known&quot; exceptions should be caught. Now, this sometimes leads to unnecessary repetitive code, for example: try {     WebId = new Guid(queryString[&quot;web&quot;]); } catch (FormatException) {     WebId = Guid.Empty; } catch (OverflowException) {     WebId = Guid.Empty; }  I wonder: Is there a way to catch both exceptions and only call the WebId = Guid.Empty call once? The given example is rather simple, as it's only a . But imagine code where you modify an object multiple times, and if one of the manipulations fails expectedly, you want to &quot;reset&quot; the object. However, if there is an unexpected exception, I still want to throw that higher. I have Solaris 8 OS installed in French.  Is it possible to switch from French to English without reinstalling the OS ? If yes how ?  When locale -a i have this :  POSIX common en_US.UTF-8 C iso_8859_1 en_CA en_CA.ISO8859-1 en_US en_US.ISO8859-1 en_US.ISO8859-15 en_US.ISO8859-15@euro fr_CA fr_CA.ISO8859-1 iso_8859_15 th th_TH th_TH.TIS620   Even when I try to edit /etc/default/init with :  LANG=en_US.ISO8859-15 LC_COLLATE=en_US.ISO8859-15 LC_CTYPE=en_US.ISO8859-15 LC_MESSAGES=en_US.ISO8859-15 LC_MONETARY=en_US.ISO8859-15 LC_NUMERIC=en_US.ISO8859-15 LC_TIME=en_US.ISO8859-15 LC_ALL=en_US.ISO8859-15   and reboot : nothing happens.  To verify the result i always use date and when i reboot : i also have the date in french.  P.S : I have to do this configuration in a computer which isn't here in my office, so i have to this manipulation in a an another computer here in my office and if it works, i'll do it to the other computer.  So the computer here is configured in English and i have to switch it to French. Here is the content of my ~./dt :  C                     errorlog              sessionlogs Desktop               errorlog.old          sessions Trash                 errorlog.older        simulateur.dtwmrc appconfig             help                  startlog appmanager            icons                 startlog.old asr.dtwmrc            outils.dtwmrc         startlog.older bin                   palettes              tmp bookmarks             sdtfonts              types dtwmrc                sdtpcaction.conf      wsmenu en_US.ISO8859-15      sdtpcaction.conf.bak   Thanks What is -crf used for in ffmpeg When converting an array of jpegs to a video file (ogg format) I have been using the -crf option.  What are the valid ranges for -crf? Currently I am using 23.    I cannot find the bookmark I read to know what this flag does and I have spent some time Googling around.  These are the arguments I am using at the moment:  -f image2 -r 10 -i " + _sourcePath + @"\img%05d.jpg -crf 18  -y -r 10 " + _destPath + "\\" + _filename + ".ogg" Adding only specific text from a file to an array list, part 2 - Java Making a Comment on a page without being on that page? I have a built a Wordpress site that enables comments on pages and I am using them as reviews, what I would like to do is for someone to be able to make a comment on a page without being on that page.    On the link above, the top right, there is a link that says have your say about a university, it would be good to have a HTML form and then a dropdown box of all the child pages of university-guide; which is where all the universities are stored, and then I can put my comments.php file into this.  So my HTML form appears and when a page is picked from a dropdown box, the comment will then be assigned to that page.  Any help or direction?    New Question for Toscho:  Below is your tweaked plugin to fit into my website, as you can see I have added the select option yearSelect and need this to appear when the comments appear. How would I go about doing this? - Could you provide ay help please?      &lt;?php /* Plugin Name: haveyoursay */  /**  * Call the form in your template with:  * do_action( 'wpse_67527_comment_form' );  */ add_action( 'wpse_67527_comment_form', 'wpse_67527_comment_form' );  /**  * Create a review form.  *  * @return void  */ function wpse_67527_comment_form() {     $select_id = 'page_select';     $url = 'http' . ( is_ssl() ? 's' : '' ) . '://' . $_SERVER['HTTP_HOST'] . $_SERVER['REQUEST_URI'];     $url = esc_url( $url );     ?&gt; &lt;form action="&lt;?php echo site_url( '/wp-comments-post.php' ); ?&gt;" method="post"&gt; &lt;h3&gt;Leave us your student perspective &lt;img src="/wp-content/themes/blue-and-grey/images/hmepage-tri.png"&gt;&lt;/h3&gt;     &lt;p&gt;         &lt;label for="author"&gt;&lt;?php _e( 'Name' ); ?&gt;&lt;/label&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;         &lt;input id="author" name="author" type="text" size="40" /&gt;     &lt;/p&gt;     &lt;p&gt;         &lt;label for="email"&gt;&lt;?php _e( 'Email' ); ?&gt;&lt;/label&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;         &lt;input id="email" name="email" type="text" size="40" /&gt;     &lt;/p&gt;     &lt;p&gt;         &lt;label for="&lt;?php echo $select_id; ?&gt;"&gt;             &lt;div class="clear"&gt;&lt;/div&gt;             Pick a university from the list: &amp;nbsp;&amp;nbsp;         &lt;/label&gt;         &lt;?php         // Ordered by page name automatically         wp_dropdown_pages(             array (                 'name' =&gt; 'comment_post_ID',                 'id'   =&gt; $select_id,                 'child_of' =&gt; 2,             )         );         ?&gt;       &lt;/p&gt;     &lt;div class="clear"&gt;&lt;/div&gt;     &lt;p style="margin:10px 0px 0px 0px;"&gt;Please select your year of study: &amp;nbsp;&amp;nbsp;     &lt;select name="yearSelect"&gt;     &lt;option value="1st"&gt;First Year&lt;/option&gt;     &lt;option value="2nd"&gt;Second Year&lt;/option&gt;     &lt;option value="2nd"&gt;Third Year&lt;/option&gt;     &lt;/select&gt;     &lt;/p&gt;     &lt;br /&gt;     &lt;p&gt;         &lt;textarea name="comment" cols="45" rows="8"&gt;&lt;/textarea&gt;     &lt;/p&gt;     &lt;p&gt;         &lt;?php         wp_nonce_field( 'unfiltered-html-comment_' . get_the_ID(), '_wp_unfiltered_html_comment_disabled', FALSE );         ?&gt;         &lt;input type="hidden" name="redirect_to" value="&lt;?php echo $url; ?&gt;" /&gt;         &lt;input type="submit" style="margin:15px 0px 0px 0px; padding:4px 10px;" /&gt;     &lt;/p&gt; &lt;/form&gt;     &lt;?php }  add_filter( 'comment_post_redirect', 'wpse_67527_redirect' );  /**  * Strip '#comment-number' from redirect url.  *  * @param  string $url  * @return string  */ function wpse_67527_redirect( $url ) {     $parts = explode( '#', $url );     return $parts[0]; } ?&gt; Minimize the sum of distances between two point and a circle Let's $A$,$B$ and $O$ be random point in a plane, such that they are not colinear. Let's $c$ be a circle centered on $O$, such that points $A$ and $B$ are outside of it. Find a point $X$ that lies on the circle $c$ and the sum $AX + BX$ is minimal.  First I tried to minimize the function:  $$f(x,y) = \sqrt{(A.x - x)^2 + (A.y - y)^2} + \sqrt{(B.x - x)^2 + (B.y - y)^2}$$ with  constraint $$g(x,y) = x^2 + y^2 - r^2 = 0$$  By moving $O$ to $(0,0)$ and do the same with $A$,$B$ so the relative distance will not change.  But these works when we know the coordinates of $A$,$B$ and the radius of the circle. Yet this isn't the right way because the problem is to construct that point.  Later I tried to approach using geometry.  The smallest distance from the point $A$ to the circle is the intersection of the circle $c$ and the ray $OA$, this is the same for $B$. Then we construct circles centered on $A$ and $B$ that are tangent to $c$. If the two circle intersect we'll get a common point for the both $A$ and $B$ and the distance will be minimal. Using computer I find the point X should be somewhere around the intercetion of the circle $c$ and the ray from $O$ to the new point.   Sometimes the optimal point differs just a bit and also this method fails when the two circles do not intersect each other Find $\lim_{x \to 0} (\frac{\tan(x)}{x})^{\frac{1}{x}}$ Find $$\lim_{x \to 0} (\frac{\tan(x)}{x})^{\frac{1}{x}}$$   My first idea to solve this was to try to evaluate it and then apply the L'Hospital's rule. This is what I managed to achieve: $$\left(\frac{\tan(x)}{x}\right)^\frac{1}{x}=e^{\frac{1}{x}\ln\left(\frac {\tan(x)}x \right)} $$ However, this is problematic, because the L'Hospital's rule is not applicable in the exponent, therefore my transformation was not a good shot. What transformation should I apply to get the desired form? Are unequal groups a problem for one-way ANOVA? I have data for three unequal groups: $N = 44$, $N = 354$ and $N = 347$. Is it possible to compare all three groups running a one-way ANOVA or is the first group too small? How to make blocks in spawn unbreakable in survival? So on my multiplayer server on Minecraft Education Edition I can't seem to figure out how to make the blocks in spawn unbreakable. I know adventure mode fixes that but it's a survival world. I don't want them in adventure, so how do I make the blocks in spawn unbreakable? How does range interact with the Arcane Archer's Curving Shot? One of the features of the Arcane Archer fighter subclass is Curving Shot:  At 7th level, you learn how to direct an errant arrow toward a new target. When you make an attack roll with a magic arrow and miss, you can use a bonus action to reroll the attack roll against a different target within 60 feet of the original target. [XGtE, pg. 28]  How does this interact with range? The Player's Handbook describes range as follows:  The range lists two numbers. The first is the weapon’s normal range in feet, and the second indicates the weapon’s maximum range. When attacking a target beyond normal range, you have disadvantage on the attack roll. You can’t attack a target beyond the weapon’s long range. [PHB, pg. 147]  I see at least four ways this might interact with Curving Shot:  The distance between the old target and new target is added to the shot's original range.  This may extend the range to beyond normal (in which case the new attack role must be made at disadvantage) or beyond maximum (in which case the new target is not valid).  The range of the redirected shot is only the distance between the old target and new target.  The shot has a new point of origin at the old target, so the new range will be between 0 and 60 feet, as limited by Curving Shot.  The range of the redirected shot is the distance between the archer and the new target.  If the new target is farther from the archer than the old one was, the range will be larger; if the new target is closer, the range will be smaller.  The range between the archer and old target is all that matters. As long as the distance from the old target to the new target is within the 60 feet defined in Curving Shot, the initial range between the archer and the old target is all that matters.  The initial attack is rerolled as is.    Related How to install NVIDIA driver in Ubuntu I'm running Ubuntu 13.04 on DELL XPS L501 - Nvidia GeForce GT 420M. I'm using kernel 3.9.0-030900-generic.  All kernel-headers are installed in the system.  and  I've tried the following.   Use apt-get to install nvidia-current (which download 304) &amp;&amp; load using modprobe Use apt-get to install nvidia-310 &amp;&amp; load using modprobe Download nvidia 64-bit driver nvidia-319.23 for 400M series and install Use swat-x repo to install nvidia driver   All of these failed. And I tested it everytime like this   After the module is loaded (checked from lsmod),  restarted lightdm tested from get.webgl.org  (Google-Chrome webgl support is enabled)    Problem faced with nvidia-xconfig   after running nvidia-xconfig (which writes to /etc/X11/xorg.conf), and restarting lightdm, my display res changes to 640x480. and had to remove this file to revert back to old setting Have also tried commenting out those two lines which adjusts Horizontal and Vertical Setting in xorg.conf. That just rectified the resolution. But still I wasn't able to use the graphics card (webgl).   EDIT 1: (nouveau)   Tried rebooting after each installation Removed (purge) all of nouveau* before starting.  Removed one more package (dont remember the exact name though) - xorg-xserver-blah-blah.   EDIT 2: (bitlbee)   I had bitlbee installed before. Removed that too before starting installation. When bitlbee was present, NVIDIA-3.9-x86.run (downloaded from nvidia) was not able to recognize graphics card. But it did when I removed bitlbee. (So I'm assuming here that it should work if graphics driver was installed properly)   EDIT 3: (software-properties-gtk)   sudo software-properties-gtk the Additional drivers tab is always NIL. (before and after installation) (even if the installation was successful)   Have been trying this the whole day, and done it quite a few times. None of them worked.  Need help! Is it the problem with kernel-3.9, that there are no updates for this ? Delete with Left Join in Oracle 10g How do I pass variables and data from PHP to JavaScript?