I am really unsure of how to answer this as I have tried taking out n and using the ratio lemma and am still confused!
I have two limit problems which are quite similar, so I've put them both into this post.   $((4^{10}+2^{n})^{\frac{1}{n}})$ $((3n^{2}+n)^{\frac{1}{n}})$   Attempt:  For 1, I'm not sure if this is permissible. I know that $\lim_{n \to \infty}(x^{n}+y^{n})^{\frac{1}{n}} = \max\{x,y\}$. Obviously $4^{10}$ is a constant so it's not quite in the same form, but I believe it is still okay to use this result, and so the limit is $2$.  For 2, I've got $((3n^{2}+n)^{\frac{1}{n}}) = (n(3n+1)^{\frac{1}{n}})$, but then I'm not too sure how to proceed.   I also thought of taking the log and proceeding that way, however in the notes I'm learning from they haven't covered l'hopital yet, so I'm trying to not use it.  Thanks.
I don't know what I've done, but all of a sudden I am unable to compile any document which uses the geometry package. Minimal (non)-working example:     \documentclass[11pt]{article}      \usepackage{geometry}  \begin{document} test \end{document}   doesn't produce any output, and this is what I see in my error summary screen in TeXnicCenter:    The red arrow points to what seems to be the problem: something about the bundle "oberdiek" and its package "ifvtex" is causing pdflatex.exe (which, while I don't really know what it does, sounds pretty important) to "not be initialized". I , and it's relevance here is a mystery to me.  I've confirmed that all of my files without the geometry package compile just fine; however, that doesn't mean that the problem is with the geometry package - what seems more likely is that there is some hidden cause of the error, and geometry happens to be one way to induce that. By the way, I've tried compiling a document which includes the ifpdf and ifvtex packages separately, and they do just fine; it's only when I include the geometry package (which for some reason requires these ifpdf and ifvtex packages) that the error occurs.  I've tried the only things I can think of:   going into MiKTeX Package Manager (by the way I am using 2.8), and removing + reinstalling both geometry and oberdiek refreshing the file name database ("FNDB") deleting all automatically generated files, as well as simply starting over in a new document   So I'm stuck now. I've considered attempting to just get rid of all traces of MiKTeX and TeXnicCenter from my computer and starting over, but that seems a bit excessive - after all, the geometry package was working for me . I honestly am not sure what I did to cause this; I've spent today trying to make a better template file for myself, and so I've been trying out new packages, but if I'm not loading these new packages there shouldn't be any conflicts, right?   Actually, I've just now thought of something that I think I did between the last time it worked and now, so is a possible candidate for the cause: I had to install some package manually, as it wasn't available on MiKTeX, and so I created a folder and pointed MiKTeX to it (i.e. the second option ). The package didn't do what I wanted, so I deleted the folder and removed it from the list of folders I told MiKTeX to check. Perhaps it's still trying to reach it for some reason? Let's say I have some XML like this  &lt;channel&gt;   &lt;item&gt;     &lt;title&gt;This is title 1&lt;/title&gt;   &lt;/item&gt; &lt;/channel&gt;   The code below does what I want in that it outputs the title as a string  $xml = simplexml_load_string($xmlstring); echo $xml-&gt;channel-&gt;item-&gt;title;   Here's my problem.  The code below doesn't treat the title as a string in that context so I end up with a SimpleXML object in the array instead of a string.  $foo = array( $xml-&gt;channel-&gt;item-&gt;title );   I've been working around it like this  $foo = array( sprintf("%s",$xml-&gt;channel-&gt;item-&gt;title) );   but that seems ugly.  What's the best way to force a SimpleXML object to a string, regardless of context? Why draw blood from veins rather than arteries? Why draw blood from veins rather than arteries? Is it more convenient or safer? Using congruences, show $\frac{1}{5}n^5 + \frac{1}{3}n^3 + \frac{7}{15}n$ is integer for every $n$ How can I find out when Windows was last restarted? How can I know when my computer running Windows 7 was last restarted?   I prefer a solution that doesn't involve searching the event log, but something like wmic or maybe cmd commands. Tensors are mathematical objects that are needed in physics to define certain quantities. I have a couple of questions regarding them that need to be clarified:   Are matrices and second rank tensors the same thing? If the answer to 1 is yes, then can we think of a 3rd rank tensor as an ordered set of numbers in 3D lattice (just in the same way as we can think of a matrix as an ordered set of numbers in 2D lattice)? facing difficulty to create dynamic xpath for City field of UTest website I am beginner in automation field, I am trying to automated one of the module, I have tried many different XPATH to fetch proper XPATH for City field o UTest site. Im trying to automate registration module as one of my assignment. I have tried my different xpath example below:  //xpath="//body/div[@class='pac-container pac-logo']/div/span[2]/span" //div[@class='pac-item']/span[3] //div[@class='pac-item']/span //div[@class='pac-container pac-logo']/div/span[2]/../span[3]   the following code written:  //xpath to send data in field @FindBy(xpath="//input[@placeholder='Enter a location']") WebElement city;  //xpath for list to appear @FindBy(xpath="div[@class='pac-item']/span") List&lt;WebElement&gt; City;  public void EnterSignupTwo(String CiTy) throws Exception {     city.clear();     city.sendKeys(CiTy);     Thread.sleep(3000);     System.out.println("the size of List " +City.size());//printing list size      for(int i=0; i&lt;City.size(); i++ ) {         String cities = City.get(i).getText(); //storing list element in String         System.out.println("Converted value of city :"+cities); //print of total list      if(cities.contains(CiTy)) //if parameterized match with Available then click     {         System.out.println("enter specific value of city :"+City.get(i).getText());         City.get(i).click();         break;     } }   kindly refer the How common is "thrice"? Kinetic energy conservation in collision.  In any type of collision type of collision if we take the system to comprised of both bodies then the net external force is zero. So the work done by external force is also zero. By the relation $W=K_f-K_i$ as $W$ is zero hence kinetic energy is conserved. But this not the case.   Can you tell me what is the flaw in my argument? Some people say that the argument has neglected the fact that some kinetic energy is transformed into heat. But heat is created due to the interactions between bodies during collision which is thus an internal force and thus shouldn't affect kinetic energy. Are there areas of mathematics (current or future) that cannot be formalized in set theory? I often read that ZFC can formalize "most" of everyday mathematics, but I could never find an example which it cannot. The closest I got is differential geometry (DF), where some article mentions that the translation from concepts of DF into set theory would render it almost "meaningless", in the sense that any intuitions one could have would be lost in the translation. So, if I didn't misunderstand, at least in theory, the translation could be done, so that a future AI machine could prove theorems of differential geometry using set theory. On the other hand, the Stanford Encyclopedia of  Philosophy states that "all of mathematics can be reduced to a formal system of set theory"().   So, the questions are:    Is there any current area of mathematics that could be not formalized within set theory? If so, which ones? and  Is there any reason to think that every math of the future will be always formalizable in set theory? any references to read on the subject are welcomed!   Clarification: by set theory I am not restricting to ZFC, but to any flavor of it, including all additional axioms you want (about large cardinals or any kind) How do I mount a partition with UFS filesystem (FreeNAS) in Ubuntu 11.10?  I'm a total Ubuntu newbie and just switched from FreeNAS.  There should be ll the info I need I guess, but if anyone would help me get going i'll by glad =) Change the display scaling on the fly I'm looking for a keyboard shortcut or a CLI instruction to change the display scale on the fly. Seems there's nothing in compiz-config manager to handle this? I want to update Acrobat Reader for Firefox, but the download has the .bin extension. How can I install it? How do they compute the Gold and Elixir that can be looted? How do they compute the Gold and Elixir that can be looted from a base? Is it 100% of the remaining? or the total (including the uncollected from mine)? Got a bunch of .mp4 videos (info shows H.264 Video + AAC Audio) that are chapters of a larger video.  I'd like to merge them, but not sure which is the best way.  I don't have Quicktime Pro, but I'll get it if that's the best way to do this.  Edit: Just to clariify this is Mac OSX 10.6 I'm on. Show finite complement topology is, in fact, a topology Linux genisoimage Batch I was practicing with modeling a leaf using a image reference. Everything went fine and I finished modeling my leaf, but I wanted to make it more realistic (I'll add textures later), I saw lots of people using the Subdivision Surface modifier but it doesn't work for me.  My model:   My model when I add the Subdivision Surface modifier DNS Resolution for example.com - Can you explain? I'm trying to install KDE 5 on my Ubuntu 16.04 system as per the instructions in , but I'm getting the below error message when running sudo apt-get install kubuntu-desktop.  Is there something I can do to resolve this?  Need to get 682 kB/326 MB of archives. After this operation, 1,272 MB of additional disk space will be used. Do you want to continue? [Y/n] y Err:1 http://ir.archive.ubuntu.com/ubuntu xenial/universe amd64              gtk2-engines-oxygen amd64 1.4.6-1ubuntu1   Temporary failure resolving 'ir.archive.ubuntu.com' Get:2 http://ir.archive.ubuntu.com/ubuntu xenial/universe amd64              libkf5sendlater5 amd64 4:15.12.3-0ubuntu1 [45.2 kB] Get:3 http://ir.archive.ubuntu.com/ubuntu xenial/universe amd64              libthreadweaver4 amd64 4:4.14.16-0ubuntu3 [46.6 kB] Get:4 http://ir.archive.ubuntu.com/ubuntu xenial/universe amd64              libfarstream-0.2-5 amd64 0.2.7-0ubuntu1 [192 kB] Fetched 284 kB in 1min 9s (4,093 B/s)         E: Failed to fetch http://ir.archive.ubuntu.com/ubuntu/pool/universe/g/             gtk2-engines-oxygen/gtk2-engines-oxygen_1.4.6-1ubuntu1_amd64.deb               Temporary failure resolving 'ir.archive.ubuntu.com'  E: Unable to fetch some archives, maybe run apt-get update or              try with --fix-missing?