Accoring to webmasters tools (sitemaps), the number of pages for one of my sites in the Google index has been steadily declining over the last few days.  In the space of a week the number of pages has dropped from over 1000 to just over 400.  Why might this be?  Has anyone else experienced something similar recently?
I am monitoring the number of pages indexed by Googlebot for one of my websites .  I noticed that since last week, the number of pages has dropped by about 60 or so. Now to be fair, I have not added that much over the last week. (Actually I don't think I added any new content.) But at the very least, I would have thought that the number of indexed pages would be static (if I was not adding anything new.)  I don't understand why the numbers have dropped.  Does anyone have an official explanation for this?. I have checked the Google Webmaster Tools, and have not come across anything that addresses this issue directly.
Find the limit $ \lim_{x \to \infty} \frac{e^{x}}{(1+\frac{1}{x})^{x^{2}}} $ Find the limit $$ \lim_{x \to \infty} \frac{e^{x}}{(1+\frac{1}{x})^{x^{2}}}. $$  I know that the limit is of indeterminate form type $\frac{\infty}{\infty}$, but it seems using L'Hopital's rule directly does not help here.  Do I somehow use the fact that $\lim_{x \to \infty} (1+\frac{1}{x})^{x}=e$? Change default code page of Windows console to UTF-8 Currently I'm running Windows 7 x64 and usually I want all console tools to work with UTF-8 rather than with default code page 850.  Running chcp 65001 in the command prompt prior to use of any tools helps but is there any way to set is as default code page?  Update:  Changing HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\Nls\CodePage\OEMCP value to 65001 appear to make the system unable to boot in my case.  Proposed change of HKEY_LOCAL_MACHINE\Software\Microsoft\Command Processor\Autorun to @chcp 65001&gt;nul served just well for my purpose. (thanks to ) How do I enable the "Universe" repository? How do I disable auto-maximizing of newly launched windows in GNOME? Each time I open any application, it zooms to fill-up the entire desktop and so I am always forced to use "Unmaximize" using Alt+Space menu. How to find the sum $$\sum^n_{k=1} (k^2+k+1)k!$$  What I tried as follows :   $$\sum^n_{k=1} (k^2+k+1)k!$$  =$$\sum^n_{k=1} (k^2)k!+ \sum^n_{k=1} (k)k! + \sum^n_{k=1} (1)k!$$  Now we can write $\sum^n_{k=1} (k^2) $ as $$\frac{n(n+1)(2n+1)}{6}$$ but what to do with $k!$ please guide thanks....... How can I produce the codes to get the symbols of pencil, ruler and compass in LATEX? I'm gonna write a sentence I can draw this figure by using simple tools in my presentation. So I prefer to include symbols pencil, ruler and compass instead of the words simple tools. Is it possible? I reviewed  in the First Posts queue.  Which said      i changed it to 'localsystem' and done. thanks much   So it obviously was a potential low quality post. But sometimes such answers can be spot on, so I checked it out, better safe than sorry. I turned out the post had been deleted. Great! So I clicked "No action needed". Then I got this:    You can imagine I felt "wrongfully accused".  I think that deleted posts should not be used for review audits, because the meaning of "No action needed" is not clear in this context. How do I prove the sequence $x_{n+1}=\sqrt{\alpha +x_n}$, with $x_0=\sqrt \alpha$ converges? ( boundedness?) If a set is $F_\sigma$ and is of first category then it is a countable union of closed nowhere dense sets We say a set is $F_\sigma$ if it is a countable union of closed sets. We say a set is of first category if it is a countable union of nowhere dense sets.  The question is, if a set of $F_\sigma$ and of first category, is it true that this set is a countable union of closed nowhere dense sets. The hydrogen protons undergo quantum tunnelling in the the sun to fuse into helium, but are only able to do so as they are under immense heat and pressure and the protons and electrons get separated. But our digestive system also makes use of quantum tunnelling to quicken the digestive process, but how do the enzymes free up the electrons when our body temperature is so low? Minecraft crashes on launch with EXCEPTION_ACCESS_VIOLATION, Problematic frame: ig4dev32.dll or ig4dev64.dll or ig4icd32.dll or ig4icd64.dll When I try to launch Minecraft 1.7.4 or newer, the game crashes on startup, and the game output screen says this:  #  EXCEPTION_ACCESS_VIOLATION (0xc0000005) at pc=*, pid=*, tid=* # # JRE version: Java™ SE Runtime Environment (7.0_51-b13) (build 1.7.0_51-b13) # Java VM: Java HotSpot™ Client VM (* mixed mode, sharing windows-* ) # Problematic frame: # C  [ig4dev32.dll+0x3e88] OR # C  [ig4dev64.dll+0x55ec] OR # C  [ig4icd32.dll+0x104a77] OR  # C  [ig4icd64.dll+0x84930a]   This happens with both Java 7 and 8.  What causes this error, and what can I do to fix the issue? Prove that if $(ab)^i = a^ib^i \forall a,b\in G$ for three consecutive integers $i$ then G is abelian Disable Mac startup sound Anyone know how to disable that cheesy startup sound when I power on my Mac?  If it makes a difference, I'm running Mac OS X 10.6. How are the measurements used by Nielsen evolving to meet new methods of content delivery and viewing? I was interested to find out that in the 1950s, Nielsen used devices in the homes of the families that were surveyed to record their viewing preferences, and only later introduced their system of using a diary to record habits:  ...in 1950...This information was collected on a device that was attached to a television that recorded what was being watched.  In 1953, the company began sending out diaries to a smaller sample of homes (“Nielsen families”) within the survey to have them record what they had watched from   So, presumably as multiple different viewers in the home were considered in the sample, the means through which the ratings were recorded changed. Given that so many people are able to record shows digitally and watch when convenient and that so many view their favorites on outlets such as iTunes, how have the Nielsen ratings systems adapted (or how does the company plan to adapt them) to capture our modern viewing preferences? While a DVR-recorded show still technically makes its original &quot;timeslot&quot; relevant to the equation, will Nielsen consider timeslot-specific data a hindrance to comparisons between those shows viewed on cable and the same show viewed on iTunes? How to type en-dash and em-dash in Windows 7/8? I write blog posts, and I often need to type en-dash (–) and sometimes em-dash (—) in my blog posts. Currently I keep these characters saved in a text file, and copy-paste them whenever I need them. Unnecessary to say, it is a headache to move between keyboard and mouse when you type large texts.  It would be better for me if there ware a keyboard shortcuts available for these two characters. Is there a way to type en-dash and em-dash in Windows? I use Windows 7 and Windows 8 in different computers.    Here's an aligned comparison of dashes, if you need to see the difference for some reason.   Here's-dash Here's–en-dash Here's—em-dash Disk Utility won't Unmount HD for formatting What’s the real-world origin of the name Azor Ahai? Azor Ahai is some mythical hero, who may or may not coincide with other mythical heros that are supposed to be born and save us from the eternal night (which is dark and full of terrors, if we are to believe Melisandre).  But I'm interested in the origins of the name, here, in our world. More specifically because in Hebrew "Azor Ahai" means (albeit ungrammatically) "Help my brothers", or if you transliterate it differently you'd get "The Living Help".   Since writers often take meaningful names to be terms from other languages (and mangle them a bit), I can't help but wonder Did GRRM reveal the origin of the name "Azor Ahai" at some point? A uncharged capacitor $C$ is connected to a battery with potential $V$. It becomes fully charged and has a charge $Q=CV$ stored on it.   Now the polarity of the battery is reversed. The capacitor will have the charge $Q$ still but with polarity reversed too.  My question is: What is the work done by the the battery?  According to me, during 1st charging it will do a work of $QV$. The energy of the capacitor is also not changing, then what is the work done to change its polarity? Can I get US sales taxes refunded for electronics purchased while on vacation? I would love to identify a sci-fi novel I read in the late 60s or 70s.  It followed a group of young space cadets through their training in the Space Academy.  The training culminated in small groups of cadets being sent through a gateway in the space station, into different worlds where they had to survive whatever conditions they met beyond the gateway, as part of their training.  One such trip went wrong and the group ended up stranded in a hostile world for days, hoping to be rescued by their trainers.  I can't remember much about the story or protagonists so this may be too vague, but I remember descriptions of a vast space station hall and these young cadets bringing whatever kit they hoped they might need - some brought breathing apparatus and full survival gear, but others came with very little as they believed they would not be sent into conditions where they could die without the right equipment.  They hadn't bargained for the power surge or whatever it was that misdirected them as they passed through the gateway!  I also remember rivalry between the cadets - I think the hero was male and quietly heading for top cadet of the year award... and I think at least one of the group died in the unknown planet before they were rescued.  Does this ring a bell with anyone?  I remember the mood and tension more than the details but it was a long time ago!  I have a 10-year old son who I think would love this kind of story.  If anyone can help you have my thanks!