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Unable to play MP3 or MP4 files in Rhythmbox or Movie Player I am unable to play any MP3 or MP4 files. When I try to open any MP3 or MP4 file, both show an error, a Python 2.7 plug-in is required. Find all continuous functions satisfying $\int_0^xf=(f(x))^2+C$ for some constant $C \neq 0$. Find all continuous functions $f$ satisfying   $$\int_0^xf=(f(x))^2+C$$ for some constant $C \neq 0$, assuming that $f$ has at most one $0$.  I have a question about the solution to this problem. It says that   Clearly $f^2$ is differentiable everywhere, its derivative at $x$ is $f(x)$ (I'm assuming that this is because the left hand side is differentiable, the right hand side must be differentiable as well). So $f$ is differentiable at $x$ whenever $f(x) \neq 0$, and  $$f(x)=2f(x)f'(x),$$ so $f'(x) = \frac{1}{2}$ at such points. Thus, $f= \frac{1}{2}x+b$ for some $b$ on any interval where it is non-zero; if $f$ has a zero, this gives two possible solutions, with two possible values of $b$, but since $f$ is assumed continuous, they must be the same. So we need $$\int_0^x(\frac{1}{2}t+b)dt=(\frac{1}{2}x+b)^2+C$$  so we must have $b=\sqrt{-C}$ or $-\sqrt{-C}$, leading to two solutions for $C \lt 0$.  I don't understand the bolded statements. First, how does the differentiability of $f^2$ guarantee that $f$ is differentiable, and why only at $x$ where $f(x) \neq 0$?  Next, why are there two possible solutions if $f$ has a zero, but since $f$ is continuous they must be the same?  Finally, does the last statement mean that if $C \gt 0$, then there is no solution, since we're restricted to real numbers here?  I would appreciate it if anyone answers my questions. I'm playing around with height maps (bitmaps), trying to create some of my own in my game, and for that I need to implement some basic drawing methods. I've quickly realized that drawing straight lines isn't as basic as I thought.  It simple's if your points share an X or Y coordinate, or if they are aligned so you can draw a perfectly diagonal line. But in all other cases its trickier.  What algorithm do you use to determine what pixels need to be coloured for it to become a "straight" line ? First, my apologies if this has already been asked/answered.  I wasn't able to find this question via search.  My question comes from Rudin's "Principles of Mathematical Analysis," or "Baby Rudin," Ch 1, Example 1.1 on p. 2.  In the second version of the proof, showing that sets A and B do not have greatest or lowest elements respectively, he presents a seemingly arbitrary assignment of a number $q$ that satisfies equations (3) and (4), plus other conditions needed to show that $q$ is the right number for the proof.  As an exercise, I tried to derive his choice of $q$ so that I may learn more about the problem.  If we write equations (3) as $q = p - (p^2 - 2)x$, we can write (4) as   $$ q^2 - 2 = (p^2 - 2)[1 - 2px + (p^2 - 2)x^2]. $$  Here, we need a rational $x &gt; 0$, chosen such that the expression in $[...]$ is positive.  Using the quadratic formula and the sign of $(p^2 - 2)$, it can be shown that we need   $$ x \in \left(0, \frac{1}{p + \sqrt{2}}\right) \mbox{ for } p \in A, $$  or, for $p \in B$, $x &lt; 1/\left(p + \sqrt{2}\right)$ or $x &gt; 1/\left(p - \sqrt{2}\right)$.  Notice that there are MANY solutions to these equations! The easiest to see, perhaps, is letting $x = 1/(p + n)$ for $n \geq 2$.  Notice that Rudin chooses $n = 2$ for his answer, but it checks out easily for other $n$.  The Question:  Why does Rudin choose $x = 1/(p + 2)$ specifically?  Is it just to make the expressions work out clearly algebraically?  Why doesn't he comment on his particular choice or the nature of the set of solutions that will work for the proof?  Is there a simpler derivation for the number $q$ that I am missing? The classic example... $X \sim Po\left (\lambda\right ), Y \sim Po\left (\mu\right)$, X and Y are independent.  Show that the conditional distribution of X is binomially distributed. Or in other words, $P(X=k\mid X+Y = n) = P (\tilde{X} = k), \tilde{X} \sim B\left (n ,\frac{\lambda}{\lambda + \mu}\right )$.   I've so far managed to reach to this step, and have been stuck since. Just somehow gotta get a $\frac{1}{n!}$ in the denominator, that would then complete the proof..or at least I think..  $$P(X=k\mid X+Y=n) = \frac{\frac{\lambda^{k}\mu^{n-k}}{k!(n-k)!}}{P(X+Y = n)}=  \frac{\frac{\lambda^{k}\mu^{n-k}}{k!(n-k)!}}{\sum_{i=1}^{n} \frac{\lambda^{i}\mu^{n-i}}{i!(n-i)!}}$$  Thanks for the help! Does the Polyjuice Potion Dark Mark work? I was just reading Harry Potter and the Deathly Hallows, and I was wondering, when Hermione Granger changed into Bellatrix Lestrange, she should've obtained the Dark Mark, temporarily.  Now, my question is: would the Dark Mark work if pressed? How do remove the CD / DVD install as a source for apt-get packages when installing new features? I'm running a Ubuntu server (9.0.4 'Jaunty') as a VMware image.  It's a real pain on the odd occasion I need to install a new package to have to fish out the install CD-ROM, and make it available to the VMware image so I can continue the package install.  Is there any way to take the original installation media out of the list of source packages - I'm assuming all packages will be available on the internet.  Thanks. Does commutativity imply Associativity? Does commutativity imply associativity? I'm asking this because I was trying to think of structures that are commutative but non-associative but couldn't come up with any. Are there any such examples?  NOTE: I wasn't sure how to tag this so feel free to retag it. I'm looking for a good, consistent and easy way to do a report of sudoers permissions for every user and group on the system. For users, I want the report to include permissions granted via group membership. What are the eigenvalues of $\operatorname{ad}x$? Let $x\in \operatorname{gl}(n,F)$ have $n$ distinct eigenvalues $a_1,\ldots,a_n$ in $F$. Prove that the eigenvalues of $\text{ad }x$ are precisely the $n^2$ scalars $a_i-a_j$ ($1\leq i,j\leq n$), which of course need not be distinct.   So we can represent $x$ by an $n\times n$ matrix $X$. We have $Xv_1=a_1v_1,\ldots, Xv_n=a_nv_n$ for eigenvectors $v_1,\ldots,v_n$.   Now, $\operatorname{ad}x$ takes $y\in \operatorname{gl}(n,F)$ to $xy-yx$. I need to show that some $y$ is taken to a scalar multiple of itself, where that scalar is $a_i-a_j$. What could be that $y$? Can you determine a formula for this problem? Why do heavier objects fall faster in air? Pre-image of a measurable set A is always measurable? I need to factory reset my Macbook but cannot recall the password. So I used Cmd+R during startup and go to terminal and typed 'resetpassword' according to this advice    Now 'Reset Password' application appears but there is nothing where I have to select the volume containing the user account. Why does this happen? How can I get around giving my mobile phone number to Google? When I want to register an account with Gmail now, it says "Google will send a text message containing a verification code to your mobile phone."  I don't want to give Google my mobile phone number!!  How do I get around this? $\lim_{n\to \infty}f(nx)=0$ implies $\lim_{x\to \infty}f(x)=0$ Can anyone help me with this problem?     Let $f:[0,\infty)\longrightarrow \mathbb R$ be a continuous function such that for each $x&gt;0$, we have $\lim_{n\to \infty}f(nx)=0$. Then prove that $\lim_{x\to \infty}f(x)=0$.   Our teacher told first to prove Baire's theorem, and then show that this is a consequence of that theorem. I proved Baire's theorem, and I spend a few hours thinking on how Baire's theorem is related to this problem, but I couldn't find anything. I'd really appreciate your help. I want to find the probability that mean is less than 5 given that poisson distribution states it is 6 ie find p(x&lt;5|x~po(6))  Here is the actual question: Two grocers agree that the daily demand for a particular item has Poisson distribution. However, grocer A claims that the mean demand is 3 items per day, while grocer B claims that the mean demand is 6 items per day. They agree to resolve the disagreement by observing the demand on one particular day: B agrees to accept A’s claim if the observed demand is 4 or less, and A agrees to accept B’s claim if the observed demand is 5 or more. (a) Calculate the probability that A’s claim is accepted when, in fact, B’s claim is correct Counting degrees of freedom of gauge bosons Gauge bosons are represented by $A_{\mu}$, where $\mu = 0,1,2,3$. So in general there are 4 degrees of freedom. But in reality, a photon (gauge boson) has two degrees of freedom (two polarization states).   So, when someone asks about on-shell and off-shell degrees of freedom, I thought they are 2 and 4. But I read that the off-shell d.of. are 3.   And my question is how to see this? Redefining \listoffigures and \listoftables as tables Chrome phishing warning on main I just got a Chrome phishing warning on main for   Is it just me, Chrome screwing things up or do you people have work to do?  The message in English:     Known phishing site detected.   Google Chrome has denied the access to stackoverflow.com. This site is reported as phishing site.      Phishing sites are designed to mislead you, so that you disclose your login credentials, password or other personal data. These sites occur as sites which you probably trust.