How to integrate $\int\frac{dx}{\sqrt{ax^2+bx+c}}$
Integrate $\int \frac{dx}{\sqrt{-ax^2 + bx +c}} $
Can someone help me figure out the big-O for the recurrence relation $T(n) = T(n^{1/2}) + 1$?  I didn't think the master theorem would work since it requires $T(n) = T(n/b)$... to have $b$ as a constant. I was wondering if anyone could shed some light on a method to approach this problem? (not looking for a solution) I know many master's students who get an opportunity to talk to their potential PhD advisors well before applying. In most cases this opportunity is available by the professors with whom they worked for their master's. Moreover, there are many others who establish a contact with professors by mailing them and enquiring about PhD vacancies.   My questions are:   How important is knowing an advisor prior to applying for PhD?  Does an email interaction play a vital role when the department makes its admit decisions? If email contact is important, can a student send out mails to 2-3 professors (working in the same area) in case one of them does not bother to reply? To sum up, is applying of any use (especially in top universities) when you have no contacts and only your credentials to bank on? There has been a trend now two persons downvote it then it goes on like that. So let there be down voting but do not display the downvotes till the user votes on it. Else the user reads it with an impression that the question is not good.  Am I missing something? Do lenses have focal planes or focal spheres/ellipsoids? This has been puzzling me for a few days now, and I asked a graphic designer I knew before trying here and haven't been able to solve it yet. It's quite weird so please bear with me for a bit.  I am using Adobe Illustrator to create a logo, and I have something that can potentially work. I have used only the pen tool with strokes (no fill), but the issue is, when I view the logo at 100%, it looks pixellated! I know vectors should not even be able to appear pixellated, but they are. Here is the screenshot from AI, without exporting to anything:     That was just done using the snipping tool within Windows, and it's at 100% zoom.  I have anti-aliasing turned on from Edit > Preferences > General, and the document resolution is at 300 ppi (I get the same result with 72 ppi).   Could anyone help me with this?   If relevant: Using CS6, and have a 24 inch Dell U2412M at 1920x1200 resolution. I do have a 21.6" Samsung at 1680x1050 and I get the same result there as well. Let me know if you need any other settings, or if you would like the file, I'd be happy to provide it to be able to solve this problem. Is it possible to create 3D red/cyan anaglyphs in a hand drawing? There are plenty tutorials online on how to create 3D red/cyan anaglyphs from existing photos in Photoshop or similar software. However, I'm wondering if it is possible to draw a 3D image by hand on for example a whiteboard using markers.  My plan is to tape together a red and blue marker and draw with it using the same rotation/inclination of the marker across the drawing. Will this give a 3D effect when viewed through red/cyan glasses? Or is the 3D anaglyph method more complex than just offsetting red and cyan lines? Hey all I downloaded this file () but can't seem to be able to uninstall it. I tried looking online as well as the README file but there is only instruction for installing, not uninstalling the package.   Attempted solutions:  sudo apt-get remove laptop_mode   returned   E: Unable to locate package laptop_mode   but when I type in laptop_mode I do get   Unhandled kernel version: 3.13 ('uname -r' = '3.13.0-32-generic')   Is there any way I can uninstall laptop-mode-tools? How are app sales/acquisitions taxed in the US? In the Ubuntu dock on Ubuntu 18.04, multiple windows of the same application are grouped and orange dots are shown to tell you how many windows of the application are opened. When you click on the icon, a small screen capture of each of the windows is shown.  However, these screen captures are shown in an order that's based on which window was last active on the desktop. This is something that clashes with the way I use the dock. I'm used to mentally mapping the windows to their dock positions. As such, I will often be trying to get to "the top one" and then I end up needing several clicks before I actually get to the terminal (or some other application) that I was looking for.  Is there some way to make sure that the order of these screen captures does not change whenever a window becomes active? Can the cometd library be used in Salesforce to listen to external buses? I'll confess up front that my knowledge of event architecture is limited:  Can the cometd library that we can use to listen for Streaming API and Platform Events also be used to listen to external (i.e. non-Salesforce) event buses?  We're hoping to make Salesforce a subscriber to replace polling integrations through the REST API. Eigenvalues of the rank one matrix $uv^T$ save as a video as .mp4 Can inner classes access private variables? class Outer {      class Inner {     public:         Inner() {}         void func() ;     };  private:     static const char* const MYCONST;     int var; };  void Outer::Inner::func() {     var = 1; }  const char* const Outer::MYCONST = "myconst";   This errors out when I compile with class Outer::Inner' has no member named `var' How can I show that the set of rational numbers with denominator a power of two form a dense subset of the reals? How can I show that the set of rational numbers with denominator a power of two form a dense subset of the reals? How delete an application that is bundled with macOS? Backstory:   I am running macOS Sierra and use TextEdit a lot. The problem is that I hate the Versions save schema that causes the universal Save As shortcut of CmdShiftS to instead create a copy of the document. I also hate how Auto-Save makes permanent changes to documents I don't want to modify when I'm tentatively modifying a work-in-progress. Since the introduction of these nuisance features in Lion I have always backed up and then replaced TextEdit.app with the legacy 1.6 version from Snow Leopard.  The problem:  Today when I tried to delete TextEdit.app from my Applications folder using this Terminal command  sudo rm -rf /Applications/TextEdit.app   I got this error  rm: TextEdit.app: Operation not permitted   I was surprised to find that I can't kill it, even with sudo.  How can I actually get rid of an application that is bundled with macOS?  What I've tried so far:  I followed the instructions in , but it didn't work. I also read , which almost accomplishes the same solution by means of disabling Versions and Auto-Save, but then I don't get the benefit of legacy TextEdit's temporary backup saving feature. See the part in the answer stating "This effectively disables the old-style, pre-Lion autosaving completely".   So I think deleting the newer TextEdit v1.12 and replacing it with the legacy v1.6 is still the best option, however I can't get my system to delete it. Any help appreciated. Determining a tricky limit What is the limit of   $$\lim_{n \to \infty} \frac{\log n}{n^\delta}$$  where $\delta &gt; 0$? (Reference : Fraleigh, A first course in abstract algebra)     Prove that a nonempty set $G$, together with an associative binary operation * on $G$ such that $a*x=b$ and $y*a=b$ have solutions in G, $\forall a,b\in G$, is a group.   Because * is an associatie operation, we have to prove that: there exists $e\in G$ such that $e*a=a=a*e$ for any $a\in G$, and that for any $a\in G$ there exists $\alpha \in G$ such that $a*\alpha=e=\alpha *a$.  This is very confusing, first I tried to prove the identity exists. If we consider a=b, then $a*x=a=y*a$, and because of the hypothesis $x,y\in G$ always exists, now we have to show that $x=y$, but I just can't do this with out inverses, so I tried to prove that the inverses exists, however I have no idea how the identity looks like, I'm stuck.  And I tried to get unstuck, so I thought particular cases, first if $G$ had only one element, then what would happend if it had just two elements... but I remembered that we don't know if G is finite or not, and I think this makes things a little bit more complicated.  What can I do? Why $\sum_{k=0}^m x^k $ is equal to $\dfrac{x^{m+1}-1}{x-1} $? Who can help me proving this (but you can no longer use $\sum$ in the proof):  $$\sum_{k=0}^m x^k=\dfrac{x^{m+1}-1}{x-1}$$ Best WPF open source projects I have programmed with WPF for more than a year. When I started there weren't so many examples and guidelines to follow, now the situation is much more better.  I would like to ask you some help in listing the best WPF (open) source code examples or projects that you suggest to study in order to learn more about project structure, best practices, etc.  Thank you, Marco What is the final price if the bid price exceeds the ask price in an order driven market?