Find the maximum of $f(x) =\int_0^x\sqrt{(x^2-x)^2+y^4}\, dy, x\in[0,1].$
Find the maximum value of $ f(x) = \int^{x}_{0} \sqrt{(x^2-x)^2+y^4}~dy$
Some compound words are written without hyphens (nonaggression, nonbeliever), some with hyphens (well-intentioned), and others with spaces (post office).  Is there a rule or good guide as to which option should be used? I suspected that installing xfce4 cause some issues in Ubuntu so I removed them using apt-get remove xfce4 xfce4-goodeis.  But when I ran 'dpkg -l' I still can see some libraries and packages for xfce4:  $ dpkg -l | grep -i xfce rc  libexo-1-0:amd64                              0.10.2-2                                 amd64        Library with extensions for Xfce rc  libgarcon-1-0                                 0.2.1-1                                  amd64        freedesktop.org compliant menu implementation for Xfce rc  libxfce4ui-1-0                                4.11.0-0ubuntu1~ppa0.13.10.1             amd64        widget library for Xfce - Gtk+2 variant rc  libxfce4ui-common                             4.11.0-0ubuntu1~ppa0.13.10.1             all          common files for libxfce4ui rc  libxfce4util6                                 4.10.1-1                                 amd64        Utility functions library for Xfce4 rc  libxfcegui4-4                                 4.10.0-2                                 amd64        Basic GUI C functions for Xfce4 rc  libxfconf-0-2                                 4.10.0-2                                 amd64        Client library for Xfce4 configure interface rc  mousepad                                      0.3.0-2                                  amd64        simple Xfce oriented text editor rc  thunar                                        1.6.3-1ubuntu1                           amd64        File Manager for Xfce rc  xfce4-appfinder                               4.10.1-1                                 amd64        Application finder for the Xfce4 Desktop Environment rc  xfce4-clipman                                 2:1.2.3-2ubuntu1                         amd64        clipboard history utility rc  xfce4-mixer                                   1:4.10.0-1ubuntu2                        amd64        Xfce mixer application rc  xfce4-notes                                   1.7.7-3ubuntu2                           amd64        Notes application for the Xfce4 desktop rc  xfce4-panel                                   4.10.1-1ubuntu1                          amd64        panel for Xfce4 desktop environment rc  xfce4-power-manager                           1.2.0-2ubuntu1                           amd64        power manager for Xfce desktop rc  xfce4-session                                 4.10.1-1ubuntu1                          amd64        Xfce4 Session Manager rc  xfce4-settings                                4.11.1-0ubuntu1~ppa0.13.10.1             amd64        graphical application for managing Xfce settings rc  xfce4-terminal                                0.6.2-3ubuntu1.1                         amd64        Xfce terminal emulator rc  xfce4-volumed                                 0.2.0-0ubuntu1                           amd64        volume keys daemon rc  xfdesktop4                                    4.11.2-0ubuntu1~ppa0.13.10.1             amd64        xfce desktop background, icons and root menu manager rc  xfwm4                                         4.11.1-0ubuntu1~ppa0.13.10.1             amd64        window manager of the Xfce project   I copy-pasted all these packages\libraries to form an apt-get remove command to remove all of these dependencies, and the command ran normally, but running dpkg -l | grep -i xfce showed these dependencies again !  Why are these dependencies still installed ? How can I reset my menus? An Olympiad problem in prime numbers :can we proof that "n" is prime in this case " Let x,n ∈ $\mathbb{N}$  such that :  1+$x^1$+$x^2$+$x^3$+....+$x^{n-1}$ is prime .  Proof that n is prime .  I actually suppose that n isn't prime absurdly so n=p×k such as p is prime ,I also use the $a^n$-$b^n$ formula  and find that $x^k$-1/$x^1$-1 so that means that k=1 and then  n=p which is absurd. Does Anyone has another answer ? Is there a way to override class variables in Java? When I call Response.Redirect(someUrl) I get the following HttpException:     Cannot redirect after HTTP headers have been sent.   Why do I get this? And how can I fix this issue? How do you explain the value of native files to an uneducated client? If you design a piece for print. It gets reproduced several times over the course of a few years. Then the client doesn't return for any work for a few more years. And suddenly you are contacted asking for native files (Indesign, Illustrator, Photoshop). As the client puts it, "We just want to be able to make minor changes, we aren't designers."  Now, there is absolutely value in the native files. They are my "secret recipe" as a designer and anyone asking for that recipe should provide compensation for the ease of reusing, repurposing, and altering the recipe.  How do you explain to this client that there is value in the native files?  How do you counter the "But we already paid for the design." argument?  Note: I know I own the files. I know my contract states I own the files. Heck even without a contract, US Copyright law states I own the files.  What I'm seeking is an elegant, less argumentative, method of explaining the file ownership to the uneducated client. Reciting legal statutes and contract clauses doesn't often make for friendly client relations. My goal is to find a method of explaining so it is fully understood by the client without the appearance of a contract clause which forces them to do something against their will. I want the client to respect and not resent these types of contract clauses. How do I get my C# program to sleep for 50 milliseconds?  This might seem an easy question, but I'm having a temporary brain failure moment! Decoupling capacitors: what size and how many? From what I understand, the  states that there is a fundamental natural limit to how accurately we can measure velocity and momentum at the same time. It's not a limit on equipment but just a natural phenomenon.  However, isn't this just an observational limit? There is a definite velocity and momentum, we just don't know it. As in, we can only know so much about the universe, but the universe still has definite characteristics.  Considering this, how do a wide range of quantum mechanical phenomena work? For example, quantum tunneling - its based on the fact that the position of the object is indefinite. But the position is definite, we just don't know it definitely. Or the famous light slot experiment? The creation of more light slots due to uncertainty of the photon's positions?  What I am basically asking is why is a limit on the observer, affecting the phenomenon he is observing? Isn't that equivalent to saying  because we haven't seen Star X, it doesn't exist? It's limiting the definition of the universe to the limits of our observation! The $ l^{\infty} $-norm is equal to the limit of the $ l^{p} $-norms. Story about a sentient star system, in a 50s or early 60s anthology Story about a sentient star system, possibly in f&amp;sf anthology from 50s or early 60s. I know this is a long shot, but I hope someone will know of this story.  I believe it was called "Darkness or into the darkness". End of the story had it spinning off a galaxy, (possibly ours?). Suppose that $f : \mathbb{C} \to \mathbb{C}$ is entire. Let $\Omega = \{ z : \frac{1}{2} &lt; |z| &lt; 2\}$. Furthermore, suppose that $ \mathcal{F} = \{f(kz) : k \in \mathbb{C}\}$ is a normal family of analytic functions defined on $\Omega$; the family $\mathcal{F}$ is normal on $\Omega$ iff each sequence from $\mathcal{F}$ has a subsequence converging uniformly on compact subsets of $\Omega$. Prove that $f$ is a polynomial.  I'm studying for my qualifying exam in complex analysis, and this question appears on an old exam. Usually, when I want to show that some entire $f$ is a polynomial, I just try to show that there exists some $N$ so that $f^{(k)}(0) = 0$, all $k \ge N$, but I'm having trouble getting that strategy to work here. I've been looking at the sequence $f(\frac{z}{n})$ trying to make something work, but have not had any success.   I would prefer to receive a hint or two, and then I'll try to post my own solution. Thanks in advance! What is the best way to remove accents (normalize) in a Python unicode string? I have a Unicode string in Python, and I would like to remove all the accents (diacritics). I found on the web an elegant way to do this (in Java):  convert the Unicode string to its long normalized form (with a separate character for letters and diacritics) remove all the characters whose Unicode type is &quot;diacritic&quot;.  Do I need to install a library such as pyICU or is this possible with just the Python standard library?  And what about python 3? Important note: I would like to avoid code with an explicit mapping from accented characters to their non-accented counterpart. Suppose $n$ divides $3^n + 4^n$. Show that $7$ divides $n$. Suppose $n \geq 2$ and $n$ is a divisor of $3^n + 4^n$. Prove that $7$ is a divisor of $n$.  My work so far:  I had a hypothesis that if $n| 3^n + 4^n$, then $n = 7^k$ for some $k\in\mathbb{N}$. But this is not necessarily so. Take $n = 7⋅379$, where $3^7 + 4^7 = 7^2⋅379$. Then, $3^7+4^7$ divides $3^n + 4^n$, and since $n$ divides $3^7+4^7$, we must have $n|3^n+4^n$. Is the use of "one of the" correct in the following context? Are there any other words similar to these words:  Award, Bestow, Donate, Grant, Give, Provide, Tax  ...that give a meaning of:  I freely give to you a portion what I have acquired or earned, without hesitation or expectation of anything in return. You are owed this, without question. There is no emotion involved with this transaction. It just is what it is.  For example: as a member of the Thief's Guild, 20% of everything you acquire will be ______ to the Guild.  Bestowed and Granted are very close...  Any other ideas? More Generating Functions problems I am trying to use notepad++ and regular expressions to edit a document. I have text in this format  123.45607894.165@abcd;aba 23.456@av1;084 9871.001@fab:9782581afa   And I need to get only the first part of the line , the one before the @ sign. How would I do that to get this:  123.45607894.165 23.456 9871.001 Breaking single polygon into multiple polygons? I created voronoi polygons after which I dissolved them on the basis of one attribute. Now there are cases where in for one single attribute "abc" I have3 polygons at different places with same object id. I would like to break these into 3 polygons as they are at different locations.  Is there any tool in ArcGIS Desktop or QGIS which can help me in doing that?