Show that $|ab| \le \frac 12 (a^2 + b^2 )$.
Prove the inequality $|xy|\leq\frac{1}{2}(x^2+y^2)$
Extracting Z data from point layer using ArcGIS Desktop? I have created a point layer with ~150 points. I have a DEM beneath it, which is where I have taken the X and Y values from.   Does anybody know how I can retrieve the Z values, without using the info button?  I am using ArcGIS Desktop 10. I have licences for the spatial analyst etc tools. Since Naruto failed the Genin exam so many times, doesn't that mean he's older than Sasuke and Sakura? What are the reputation requirements for privileges on sites, and how do they differ per site? Formerly Reputation requirements compared. What are the reputation requirements for privileges on the various sites in the network? Also, how do reputation requirements for various privileges compare on different Stack Exchange sites? Specifically, the following types of sites:  Designed sites e.g. Stack Overflow, Ask Ubuntu, Gaming, etc. Public beta and non-designed sites Private beta sites  ...as well as any site-specific differences. First time I've used cycles rendering engine.  I'm using a movie clip as the background in short animation. Selected RBGA under Property Tab, and Transparent under Film Tab.  It looks good and individual frames in OpenGL active viewport render, and looks fine.  When I try to get it to spit out PNG files of the finished animation the objects render out fine, except no movie clip background as Blender Render engine did when using Paper Sky setting.  Operator error, or am I trying to do something Cycles won't do?  Haven't found an answer in my searches so far.  Can anyone point me in the right direction please.   Addition:  I think I found my problem after a couple more hours of research.  Post should read "operator ignorance" instead of operator error.  Too tired to try the solution tonight, everything looks better in the morning. Thanks anyway.  Sorry, I just saw your posts.  Really tired.  Much appreciation. TeXStudio : Disable auto-completion of parentheses I cannot stand the auto-completion of TeXStudio (formerly TexMakerX) regarding parentheses, braces, etc. I agree auto-completion is useful sometimes, but here it does just not work as I would like. How can I remove it completely?  Under configuration -&gt; completion nothing is checked. From where do I remove the auto-completion of these? I'm currently building a town in Minecraft Pocket Edition and I'm wondering how many blocks long and how many blocks wide the world is. Mixing tenses in past tense fiction 'undefined reference to symbol 'pthread_create@@GLIBC_2.2.5' while compiling bochs I'm trying to compile bochs with this command:  ./configure --with-x11 --with-wx --enable-ne2000 --enable-iodebug --enable-disasm --enable-debugger --enable-e1000 --enable-usb --enable-pci   it works, but then when I run make I got:  usr/bin/ld: gui/libgui.a(gtk_enh_dbg_osdep.o): undefined reference to symbol 'pthread_create@@GLIBC_2.2.5' /lib/x86_64-linux-gnu/libpthread.so.0: error adding symbols: DSO missing from command line   Any Help ? :/ Progressive Draw 2 and Draw 4 Uno When playing with progressive Draw 2 and Draw 4 and (say that there are 2 players playing) and    Player 1 goes out with a Draw 2  Player 2 puts down a Draw 2    Does player 1 have to pick up 4 cards? Applying MVT and IVT (?) to show something about f'''? (edit: actually, Taylor's Theorem using Lagrange remainder) Why can "trans" be replaced with an x? I can't think of an example, so I may be wrong about this, but I think I've seen people replace the prefix "trans" as in transport with an x. "Cross" makes sense, as in "railroad crossing", and I guess "chris" is sort of a punny extension, the extension being like "chris cross" and the example being "xmas", but why trans? Seeking shapefile of city boundaries in US? What is the optimum pattern to place crops in Minecraft? What factors affect soil hydration and crop growth time? What is the most efficient layout of dirt and water to grow crops? `/usr/bin/cd` is not working in mac terminal How do I find the caller of a method using stacktrace or reflection? I need to find the caller of a method. Is it possible using stacktrace or reflection? Why does parameter expansion with spaces without quotes work inside double brackets "[[" but not inside single brackets "["? Storing the original document class page layout with geometry Is it possible, using the geometry package, to store (and restore) the original layout specified by the document class (in my case, the class is report)?    Here is some context.  I have been editing a long document in the default page layout for the report document class.  Now I found out that I need a title page.  There is a particular title page layout, and in fact, it works perfectly if I just load the geometry package with its default and change just two settings.  But then I want the rest of the document back in the original page layout!  I can't do something like \restoregeometry, since I think geometry just overrides the class options... i.e. there doesn't seem to be anything to restore.  Similarly, it seems I can't use \savegeometry or \loadgeometry.  So how can I get back to my original layout for the rest of the document without painstakingly hard-coding in all of the specific page layout variables?    Here is a minimum working example:   \documentclass[a4paper,10pt]{report}  \RequirePackage[a4paper,dvips]{geometry} % g1 \geometry{top=2.5cm,bottom=2.3cm}        % g2  \begin{document}  \input{the_title_page}  \SomeGeometryCommandsHere  % g3  \input{the_rest}  \end{document}   If I run the above code with the lines labeled "g" commented out, then the title page does not have the correct page layout, but the rest of the document is formatted perfectly.    If I leave lines g1 and g2 uncommented, then the title page has exactly the correct layout, but no matter what I put for g3 (e.g. \loadgeometry, \restoregeometry, etc.) I can't recover the original layout that I had when g1 and g2 were commented.  Of course, I could completely specify the original layout exhaustively in line g3, and this should in principle work.  However, I spent almost one hour on this last night and when I still couldn't get it formated correctly I decided I really needed a smarter solution. What should I do when my neural network doesn't generalize well? Ill implement the some UI but its not working in the visualpage , can u know how implement jquery ui in viusalpage ,  Kindly tell the procedure ,     Im using this url its not working ,,,,, How to handle relative urls correctly with a nginx reverse proxy