Trig limit without L'Hospital Rule: $\lim\limits_{x\to0}\frac{\tan x-\sin x}{x^3}$
Limits of trig functions
Relative pronouns "where" and "when": where can they be omitted? Doubt on Rechargable LED Emergency bulb I have recently seen a  and I  was wondering how it is working.  In the event of a power failure, the LED bulb will turn ON automatically. That is, when the switch is ON and mains power goes off the bulb will detect that and turn ON. If the switch is OFF bulb will not turn ON. When mains are ON and the switch is ON the bulb will start recharging again.  It is just like a normal bulb. See the   My question is, how the bulb will detect the event of mains failure? Can somebody give me a hint on this? How can you dynamically create variables via a while loop? Suppose I have a document with multiple include or input statements  \input{fileA} \input{fileB}   etc.   Is there an easy way to generate a single .tex file where \input{fileA} is replaced by the actual content of fileA etc. without copying it manually? Just a quick question from an Objective-C beginner: what does the asterisk in the parenthesis mean in the following sample code? Is it a pointer? Thanks in advance.  #import &lt;Foundation/Foundation.h&gt;  @interface Tire : NSObject @end @implementation Tire  - (NSString *) description {    return (@"I am a tire."); }  @end I want to block access to my web server by default as a precaution but I keep getting the following errors showing up in my error log.      [Wed Jun 27 23:30:54 2012] [error] [client 86.77.20.107] client denied by server configuration: /home/www/default/Edu.jar      [Wed Jun 27 23:32:40 2012] [error] [client 86.77.20.107] client denied by server configuration: /home/www/default/REST.jar      [Wed Jun 27 23:35:39 2012] [error] [client 86.77.20.107] client denied by server configuration: /home/www/default/Set.jar      [Thu Jun 28 01:01:17 2012] [error] [client 58.218.199.227] client denied by server configuration: /home/www/default/proxyheader.php      [Thu Jun 28 02:34:57 2012] [error] [client 58.218.199.227] client denied by server configuration: /home/www/default/proxy.php      [Thu Jun 28 05:41:33 2012] [error] [client 58.218.199.227] client denied by server configuration: /home/www/default/proxyheader.php      [Thu Jun 28 06:55:10 2012] [error] [client 180.76.6.20] client denied by server configuration: /home/www/default/      [Thu Jun 28 07:31:26 2012] [error] [client 86.77.20.107] client denied by server configuration: /home/www/default/Edu.jar      [Thu Jun 28 07:32:25 2012] [error] [client 86.77.20.107] client denied by server configuration: /home/www/default/REST.jar      [Thu Jun 28 07:36:10 2012] [error] [client 86.77.20.107] client denied by server configuration: /home/www/default/Set.jar   I don't really want these errors to show up but whatever I do, I can't get rid of them. Does anyone know how I can achieve this?  Here is a copy of my configuration.  &lt;VirtualHost *:80&gt;     DocumentRoot /home/www/default      &lt;Directory /&gt;            AllowOverride None            Order Deny,Allow            Deny from all     &lt;/Directory&gt;      #ErrorLog /var/log/apache2/error.log     #LogLevel warn     CustomLog /var/log/apache2/access.log combined &lt;/VirtualHost&gt; How to access blocked sites? I am in Pakistan and  is blocked here. I want to take the Lecture videos from YouTube. In Windows, I was using  to bypass the proxy.   But now, using Ubuntu, I don't know how to bypass the proxy. I found some where that i can bypass the proxy by using putty software. Can you guide me how can I bypass proxy by that? I tried, but I was not able to do so. Kindly tell me some easy method to bypass proxy. I don't want to used websites like accesstoblockedsites.com. Rank of the $n \times n$ matrix with ones on the main diagonal and $a$ off the main diagonal I want to find the rank of this $n\times n$ matrix \begin{pmatrix} 1 &amp; a &amp; a &amp; \cdots &amp; \cdots &amp; a \\ a &amp; 1 &amp; a &amp; \cdots &amp; \cdots &amp; a \\ a &amp; a &amp; 1 &amp; a &amp; \cdots &amp; a \\ \vdots &amp; \vdots &amp; a&amp; \ddots &amp; &amp; \vdots\\ \vdots &amp; \vdots &amp; \vdots &amp; &amp; \ddots &amp; \vdots \\ a &amp; a &amp; a &amp; \cdots  &amp;\cdots &amp; 1 \end{pmatrix}  that is, the matrix whose diagonals are $1's$ and $a$ otherwise, where $a$ is any real number.  My first observation is when $a=0$ the rank is $n$ and when $a=1$ the rank is $1.$ Then I can assume $a\neq 0, 1$ and proceed row reduction to find its pivot rows. I obtain  \begin{pmatrix} 1 &amp; a &amp; a &amp; \cdots  &amp; a \\ 0 &amp; 1+a &amp; a &amp; \cdots &amp; a \\ 0 &amp; a &amp; 1+a &amp; \cdots &amp; a \\ \vdots &amp; \vdots &amp; \vdots &amp; \ddots &amp; \vdots \\ 0 &amp; a &amp; a &amp; \cdots  &amp; 1+a \end{pmatrix} by subtracting the first row multiplied $a$ for each row below the first, and then divides the factor $(1-a)$,  and stuck there. Any hints/helps? $r$ primitive root of prime $p$, where $p \equiv 1 \mod 4$: prove $-r$ is also a primitive root question is as follows:  Let $p$ be a prime with $p \equiv  1 \mod 4$, and $r$ be a primitive root of $p$.  Prove that $-r$ is also a primitive root of $p$.  I have shown that $-r^{\phi(p)} \equiv 1 \mod p$.  What I am having trouble showing, however, is that the order of $-r$ modulo $p$ is not some number (dividing $\phi(p)$ that is LESS than ($\phi(p)$).  By way of contradiction, I've shown that the order of $-r$ cannot be an EVEN number less than $\phi(p)$.  But my methodology does not work for the hypothetical possibility of an ODD order that is less than $\phi(p)$.  Any and all help appreciated.  Happy to show methodology for any of the parts I have managed to do, if requested. Backup to Azure Storage Container: Shared Access Signature the only way? RESTORE FILELISTONLY FROM URL = '' WITH CREDENTIAL = '' fails in SQL Server 2016.  Copied script from SQL Server 2012 environment, successfully restoring from Azure Storage Container, with create credential statement, and it failed in 2016.  Error message "Forbidden".  Only after logging into the Azure Portal, creating a Shared Access Signature for the container, could I execute the restore, and only by not specifying the credential did the restore work.  No documentation advises that a SAS (Shared Access Signature) is required in SQL Server 2016 for Azure container backup / restore.  Is there another way to use T-SQL to access blob backups on Azure storage containers in SQL Server 2016, than using SAS?    Looking at the MSDN tutorial on how to configure the backup service SQL 2016 introduces, a SAS is used. Refer Script to convert filenames to lowercase depending on extension How to delete one shape from another in Illustrator CS4? I have an image (below) of two hands over a black circle. All three are currently separate paths with a fill but no stroke, all on the same layer.  How do I delete the shape of the hands from the black circle, so that afterwards I can delete the hands themselves, and just have the circle, with the shape of the hands cut out of it? Prevent Photos app on OSX from launching when plugging in device The Photos app opens whenever I plug in my phone.    How can this be prevented?  I have seen many solutions for the old iPhoto app that involve changing the "Connecting camera opens" option, but the new app has no such option. If verification is quality control, what is a validation? Debian based system, only one gui program, nothing else I would like to make a debian system where you can only open one GUI program at boot, no other graphical interface, no minimize, or any X apart from that program, is there a way to do it on debian if possible, or any other custom distro? I just want to boot open the program and allow the user to only see and use that program. Checking if array is multidimensional or not? What is the most efficient way to check if an array is a flat array of primitive values or if it is a multidimensional array? Is there any way to do this without actually looping through an array and running is_array() on each of its elements? How do I set up a Godox X2Tc to control a Canon Speedlite 430 EXII I have a Godox X2Tc and a Godox X1Rc. I want to control my Canon Speedlite 430 EXII. (I also have a Godox V1, which is a beautiful thing!) I have the Canon Speedlite attached to the Godox receiver, so it should fire. It just wont! How do I set it up correctly so the receiver makes the Canon Speedlite fire?  Update: Michael C answered this question. I had the ID numbers set differently on the transmitter and receiver. I made them the same and now it all works. Perfect! Thanks Michael!! How do I document a module in Python? That's it. If you want to document a function or a class, you put a string just after the definition. For instance:  def foo():     """This function does nothing."""     pass   But what about a module? How can I document what a file.py does? Space war, humans recreated, grown from plants with an alien female supervisor This was a small hardback book I read in the UK in the late eighties. No memory of the cover.  Some kind of space war and a long lived alien female escapes the conflict in her starship, her side had lost.  An evil enemy that she needs to trap so she gets (I think) human  DNA from space dust and sets up on a habitable planet. The story then gets like episodic and looks at the world every couple of generations while she hides out there.  Plants bud on the world and people pop out from big seedpods, the population listens out for babies crying and rescue them.  There are legends of the 'Earth mother’ who secretly guides them to become high tech.   In reality she is creating attractive food bait for the bad aliens.  I think an early human and her are attracted to each other and she (maybe) gives him long life or (maybe) uses reincarnation to keep seeing him.  Edit:- the name 'Rimstalker' has just now popped up in my brain! I have a lot of Excel sheets for all sorts of things - but none has ever acted up like this one here:    This used to be a totally normal Excel 2007 sheet which I was able to resize, maximize etc. - but not anymore. The MDI child window is fixed, both in position and size. I cannot move it around, more can I maximize it to use the full size of the screen anymore. I cannot double-click on it's title bar to maximize it either :-(  What happened? What can I do to "undo" whatever I did to it.  Any ideas? I tried to share / undo sharing, I tried to protect / unprotect the sheet - nothing seems to work...