$$ \lim\limits_{(x,y) \to (0,0)} \frac{2x^2y^3}{x^4+y^6} $$ My reasoning after reading the textbook: Direct substitution wouldn't work since it would lead to the indeterminate form $0/0$. We can examine the values of $f$ along parabolic curves that end at $(0,0)$. Along $y=kx^2, x\neq0$, the function has the value $$ \frac{2k^3x^4}{1+k^6x^8}. $$ So, if $(x,y)$ approaches $(0,0)$ along $y=x^2$, then $k = 1$, and the limit is $\frac{2x^4}{1+x^8}$. If $(x,y)$ approaches $(0,0)$ along the $x$-axis, then $k=0$, and the limit is $0$.Is this correct and/or is there another way to go about this? Thanks.
I want to determine $$\lim\limits_{(x,y) \to (0,0)} \frac{x^2·y^3}{x^4+y^6}$$  I'm sure the limit exists, it's zero because I tried to find other different limits in line and parabola points ($(x,mx)$ and $(x,mx^2)$) but every time I got zero. So, I have to use the definition or sequences to confirm.
I'm an android developer and have laptop with 4GB RAM. When I compile my project the RAM is used at 100%.    If I add more RAM will it solve the problem? What's the difference about /t̬/ and /d/? invalid EFI file path on windows 8 MacBook Pro never goes to sleep Leave Convert to Edit button enabled all the time in the moderator flag list In the moderator flags list, there is a &quot;Convert to Edit&quot; button on answers which are posted by the person who posted the question. This button is disabled at times, and I am not sure that the algorithm used is useful. My proposal is that the Convert to Edit button in the flag list should always be enabled, as it seems fairly frequent that it's disabled when it would be useful. Justification When the button is disabled, it is required that we pop open the answer view in the flag list, and use the regular Mod menu and choose convert to edit there. When we do that, however, we experience this issue:  (that should also be fixed, by the way!) Here are two items currently in the queue:    Note that one has the button enabled, while the other does not. The only differences I can see in those two answers is the age and the number of answers. Neither question has an accepted answer, but the one with the button disabled only has that single answer. I've only just now noticed that difference with these two posts, so I'm not 100% sure if that's the determining factor. 1 It is perhaps coincidental, but these buttons being (dis)abled are reverse of the action needing to be taken. The one with the disabled button needed to be converted to an edit; the one with the enabled button was an attempt to answer their own question. If I'm right about the determining factor here (that the answer is the only one), I'm not sure that's useful. A good bit of the time, an asker will post an answer due to people requesting additional information. In such cases, it seems like it will be likely there are no other answers. 1  Note 1: I was looking to create a userscript to enable these buttons, and I found something that I think is related as to the reason. It looks like the ones which are disabled are on answers which have comments on them. I noticed the title attribute of those buttons says, &quot;There are comments on the post. Please review&quot;. That does seem to make some sense in theory. However, it still seems like I am often converting them, anyway. With the above-linked, separate issue regarding how the 'mod' link on the expanded view works, this is still a bit of an impediment to our workflow. It occurred to me to check if the button was reenabled once you expanded the view, but it does not. Maybe that's an alternate solution. My plan for my userscript is to enable the button, but change the text color (and leave the title attribute), to point out that there are comments. Problem about the definition of Euclidean domain Proving that the map from a topological space to a fiber bundle is open. C++ compiling on Windows and Linux: ifdef switch I basically need to highlight a particular word in a block of text. For example, pretend I wanted to highlight the word &quot;dolor&quot; in this text: &lt;p&gt;     Lorem ipsum dolor sit amet, consectetuer adipiscing elit. &lt;/p&gt; &lt;p&gt;     Quisque bibendum sem ut lacus. Integer dolor ullamcorper libero.     Aliquam rhoncus eros at augue. Suspendisse vitae mauris. &lt;/p&gt;  How do I convert the above to something like this: &lt;p&gt;     Lorem ipsum &lt;span class=&quot;myClass&quot;&gt;dolor&lt;/span&gt; sit amet, consectetuer adipiscing elit. &lt;/p&gt; &lt;p&gt;     Quisque bibendum sem ut lacus. Integer &lt;span class=&quot;myClass&quot;&gt;dolor&lt;/span&gt; ullamcorper     libero. Aliquam rhoncus eros at augue. Suspendisse vitae mauris. &lt;/p&gt;  Is this possible with jQuery? Edit: As  , this is quite possible without jQuery - but I was hoping there might be a special method of jQuery which would let you do selectors on the text itself. I'm already using jQuery heavily on this site, so keeping everything wrapped up in jQuery would make things perhaps a bit more tidy. Using OPENQUERY to execute a script I have a SQL Server 2008 instance which I want to use to import data from an Oracle server.  I have set up a linked server that works correctly when running simple queries like SELECT * FROM table. However, if I declare a variable or loop through the rows in a table or anything else inside the OPENQUERY, I get errors.  Is it possible to do this using OPENQUERY? Do I need additional permissions? The interaction of TeX and Lua can be quite delicate at times.  While the former has category codes and tokens, the latter has escape sequences and datatypes.  Mixing the disparate concepts of these two worlds can lead to unexpected behaviour which favours common errors, known as gotchas. In the community wiki answer below you can find an overview of the common mistakes that people make when getting to grips with LuaTeX. $\phi \times \theta$ is faithful iff $(|Z(H)| ,|Z(K)|)=1$ for faithful characters $\phi \in Irr(H)$ and $\theta \in Irr(K)$ . How can one use multi threading in PHP applications Is there a realistic way of implementing a multi-threaded model in PHP whether truly, or just simulating it. Some time back it was suggested that you could force the operating system to load another instance of the PHP executable and handle other simultaneous processes.  The problem with this is that when the PHP code finished executing the PHP instance remains in memory because there is no way to kill it from within PHP.  So if you are simulating several threads you can imagine whats going to happen.  So I am still looking for a way multi-threading can be done or simulated effectively from within PHP. Any ideas? Adding console.log to every function automatically Is there a gender-neutral pronoun that can replace “his” or “her”? This post has two parts: (a) a question and (b) a proposal.   (a) Often, particularly while writing technical papers or user's manuals, I have come across a situation where I need to say:      A user of this software may not need to use it from his personal computer. He can use it from a phone or even from his tablet.   I have seen many authors use female pronouns (i.e. “she” and “her”), but lately this trend seems to have ebbed somewhat.   I, and (I suspect) many other authors, do not want to use passive voice to avoid this.   Is there a gender-neutral way to describe the same situation?   (b) If there is none, I would like to propose using “ze” (for “he” or “she”) and “zir” (for “his” or “her”, rhyming with “fir”) as gender-neutral pronouns. I want to know how you feel about these words. How do you get the index of the current iteration of a foreach loop? pygame installation issue in mac os How can I save application settings in a Windows Forms application? What I want to achieve is very simple: I have a Windows Forms (.NET 3.5) application that uses a path for reading information. This path can be modified by the user, by using the options form I provide.  Now, I want to save the path value to a file for later use. This would be one of the many settings saved to this file. This file would sit directly in the application folder.  I understand three options are available:   ConfigurationSettings file (appname.exe.config) Registry Custom XML file   I read that the .NET configuration file is not foreseen for saving values back to it. As for the registry, I would like to get as far away from it as possible.  Does this mean that I should use a custom XML file to save configuration settings?  If so, I would like to see code example of that (C#).  I have seen other discussions on this subject, but it is still not clear to me. How do I install software using the Ubuntu Software Center? The title says it all. I'd like to know how I can install software - an example is the Chromium web browser. Installing Crystal Reports 8.5 on Windows 7 I have successfully installed Crystal Reports 8.5 on my Windows 7 desktop, but when I try to launch the application i get this:    Any experience with this?  Besides the obvious "update to as newer version", does anyone have any suggestions?