Lebesgue integral of absolute value of sequence of functions
If $f_k \to f$ a.e. and the $L^p$ norms converge, then $f_k \to f$ in $L^p$
How would you prove the following limit?  $$\lim_{(x,y) \to (0,0)} \frac{x^3y}{x^4+y^2} = 0$$  I think the best way is using the squeeze theorem but I can't find left expression.  $$0 \le \frac{x^3y}{x^4 + y^2} \le \frac{x^3y}{x^4} \le \frac{x^3y}{x^3} \le y = 0.$$  But I'm not sure I'm right (especially at $\frac{x^3y}{x^4} \le \frac{x^3y}{x^3}).$  If I'm right - I'd glad if you can accept it.  If I'm wrong - can you please correct me?  Thanks in advance! WPF Binding to variable / DependencyProperty Why is free will a widely discussed, established concept? Does this concept emerge from religious / spiritual doctrine? Why is there so much interest in this topic?  If a neural-network based AI machine with a certain high degree of complexity scores a perfect 100 every run in a turing test, have we not already refuted the idea of free will? In fact, let me extend this reasoning, if ANY machine scores a single point in a turing test (and not 100), have we not already disproved (or alternatively put in great doubt the existence of) free will? If we already created a machine that can master a certain degree of human interaction, have we not then demonstrated that human interaction is programmable? (given enough time for the creation of a complex or more appropriately elaborative neural system).   From the perspective of an external observer, such a machine would be qualitatively human although intrinsically quantitative behind a stream of 1's and 0's. It would exhibit a type of decision making indistinguishable from that of a human. Does this not reduce the type of decision making we understand to be "free will" to something quantitative, deterministic, materialist? This may be a stupid or trivial question, but I am new to Ubuntu, and have two unsolved problems (flashplayer doesn't play, and scanner doesn't work - in virgin install 13.04), so I started to search in documentation. In the 13.04 specific web site I was browsing the hardware section, and came across something like this: "Open Dash, and select Disk Utilities".  So what is Dash, and where is Disk Utilities?  The application finder could not find any of those. In terminal the "dash" command seems to invoke some sort of a shell. What is the "show desktop" keyboard shortcut? I just upgraded to 11.10 from 11.04. Previously the shortcut to show the desktop was Super +D (same as in Windows), But now it is not working. What is the new shortcut? I am running Ubuntu 12.04 on an IBM ThnkPad T42.  I just installed Gnome and Cinnamon but I am still using Unity.  The only problem is that in dash when I search for any application they don't appear.  I don't see recent applications either.  I fixed it by running unity --reset but the next time I turned on my computer it was broken again This question is related to "The Last Jedi":  The maneuvre that vice admiral Holdo (with the purple hair) uses towards the end of the film seems remarkably effective.   It seems that it would have worked pretty well much earlier. Especially as two other ships were just allowed to run out of fuel and be destroyed.  It seems doing it earlier with different assets would have incurred less losses. Yet nobody seemed to consider it. Any in universe reason why? Create NSString by repeating another string a given number of times Emoji Characters I'm trying to display Emoji Characters inside my XeLaTeX Document. It seems to work for some glyphs like the numbers and pound sign but not for all. Here is a MWE:  \documentclass{scrartcl}  \usepackage{fontspec}  \setmainfont{Apple Color Emoji} % The emoji Font   \begin{document} \char"0030{}  %Works \char"1F60D{} % Doesent Work should out put SMILEY FACE WITH HEART SHAPED EYES \end{document}   What is the reason for this strange behavior and is there a way to include Emojis in XeLaTeX?  Edit:   It seems the Character is there. It is selectable but not visible. I can copy&amp;paste it. Check if specific id element exist How do I add Headers in List of Tables page? I have a button created by my script. I wonder how I can display what the system console displays but inside blender's console. CoDEmanX did this by running a script inside it as shown , but I want to display what happens in the system console inside blender's console.  My .blend file can be found here: I was wondering if $\mathbf{A}\times\mathbf{C}=\mathbf{B}$ and $\mathbf{A}\cdot{\mathbf{C}}= p$, is it possible to express C in terms of A, B, and p?  Note: A, B, C are vectors and p is a scalar.  Sorry if this question has been asked before. If so, can anyone give me a link to it? Where are the audio files of "Voice Memos" stored on macOS Mojave? There are no options for Voice Memos application to specify path to save.  Searching for the recording name also did not reveal any file in Finder.  I wish to edit the audio file in Audacity but I need to find the saved file first. "He didn't know where New Jersey was" I know the past tense carries the past tense in every dependent clause, but referring specifically to places or to things that are eternal, like the Earth, seems a bit weird and therefore we sometimes (I believe incorrectly) say     He didn't know that New Jersey was actually on the East Coast.   Because it still is. Or     He thought the Earth was round.   So is it square now?  Logically speaking, would you consider the use of past tense here a bit confusing in a day-to-day speech in these examples? Would you instinctively opt for using the present tense? How can I obtain the command line arguments of another process?   Using static functions of the System.Diagnostics.Process class I can obtain a list of running processes, e.g. by name:  Process[] processList = Process.GetProcessesByName(processName);   However, there is no way to access the command line used to start this process. How would one do that? Lost space after removing bootcamp So I removed bootcamp and now there is a partition called "free space" that I can't remove.  Here is my output from diskutil list:    Here is the screenshot from disk utility showing the partitions:    And here is the error I get when I try to remove "free space":    Heres the output when I run   sudo diskutil apfs resizeContainer disk0s2 0 I'm using Microsoft Word 2010 and I worked in a word-2003 compatible document (.doc). After hours of working, I selected a half of text and did Ctrl+X to copy it into another document. Surprising, after closing the current document and opening a new one and pressing Ctrl+V, nothing happened. After closing original document, ms word asked me if I want to save the clipboard buffer and I pressed No, as I didn't knew that MS Word has it's own clipboard.  Is there a way to recover that text that was "cutten" from original document and never "pasted" to the new one? The PC was not rebooted so i guess all my temp files are here. Let's say that a player uses the ready action and says "If a character aims at me with a weapon, I'll use Teleport to move behind cover."  What happens? Does this work? If not, please cite the rules to explain why not. We know the escape velocity from the Earth is 11.2km/s. Isn't it the velocity required to escape from earth if we go normal to the surface of earth? i.e while we derive the formula for the escape velocity from earth we never consider the slanted motion of the object. So when we launch a rocket we need to use very less value of velocity compare to escape velocity to escape from earth because rocket follows a slanted path so curvature of earth has an effect?  If what I said above is right, then how we can say escape velocity is 11.2 km/s?