PYTHON 3 function bug?
How to test multiple variables against a single value?
This is about that old chestnut, $\newcommand{\d}{\mathrm{d}} \int \sin^2 x\,\d x$.   OK, I know that ordinarily you're supposed to use the identity $\sin^2 x = (1 - \cos 2x)/2$ and integrating that is easy. But just for the heck of it, I tried using the $u$-$v$ substitution method (otherwise known as integration by parts).  $$ \int \sin^2 x\,\d x = \int \sin x \sin x\,\d x $$  We can say $u=\sin x$ and $\d u=\cos x\,\d x$ while $\d v = \sin x\,\d x$ and $v = -\cos x$. When we put it all together:   $$\int \sin^2 x\,\d x = u v - \int v\,\d u = -\sin x \cos x - \int -\cos^2 x\,\d x$$  and doing the same routine with $\cos^2 x$ we get $u = \cos x$, $\d u = -\sin x\,\d x$, $\d v = \cos x\,\d x $ and $v = -\sin x$, leading to:  $$\begin{align}   \int \sin^2 x\,\d x = uv - \int v\,\d u     &amp;= -\sin x \cos x - (-\cos x \sin x - \int -\sin^2 x\,\d x) \\     &amp;= -\sin x \cos x + \sin x \cos x - \int \sin^2 x\,\d x \end{align}$$  which eventually works out to  $$2\int \sin^2 x\,\d x = 0$$  So I wanted to get an idea why this didn't work. Maybe it's higher math and the why will be beyond me (I would think that might be the case), or maybe it's one of those proofs that looks absurdly simple when shown that I am just unaware of. QGIS 2.0 - can't select items in Print Composer I am trying to evaluate the following sum. Here $x\in\mathbb{R^{+}}$. $$f(x)=\sum_{n=1}^{\infty}\frac{(n-1)!}{\prod_{r=1}^{n}(x+r)}$$ At present I do not know how to proceed. Any hints are appreciated. Thanks. Crash adding comment "Calling dibs" - what does it imply? The term "to have dibs on something" or "to call dibs on something" plays a recurring role in American film and television (e.g. ), so it gets exported a lot.   describes "dibs" as     [...] a common, "informal" convention to reserve or declare full or partial ownership of a community resource, such as a chair [...]   From the usages in the media I have seen, this convention also seems to contain some moral concept which is not described in dictionaries. For me, it looks like by calling dibs (or ), the caller actually receives the (implicit, moral) right to that resource, and this typically goes undisputed by their rivals.  Can you confirm the existence of this concept? Is this something that varies between groups of people (or maybe between regions), or is there a concensus on how to respond to this? How does the coin limit work? Let $\{E_i\}_{i=1}^n$ be finitely many disjoint sets of real numbers (not necessarily Lebesgue measurable) and $E$ be the union of all these sets. Is it always true that  $$ m^\star (E)=\sum_{i=1}^N m^\star(E_n) $$ where $m^\star$ denotes the Lebesgue outer measure? If not, please give a counterexample. The Vitali set is a counterexample in the countable case, but I am not sure whether it is false in finite case. What are the limitations on the Shape Water cantrip? I have been having a discussion regarding the Shape Water cantrip from the Elemental Evil Player's Companion. A friend and I are trying to come to an accurate view of how this spell actually functions.   Some example questions:   Must the targeted water be within a 5 foot cube area, or does it need to be of a volume not exceeding 125 cubic feet? If you shape water that is within a 5 foot cube, can the final shape you animate it to extend outside the cube? Can you cause the shaping to affect ice and snow, or only liquid water? Would you be able to carry a globe of water alongside you over distances?   Really, there are two parts:    What can be targeted by the spell? What are the limitations on the 'shape and animate' portion of the spell?   The answer I am looking for, if possible, would use the language of the spell, possibly with precedent from other game text, to clearly define the limitations of this cantrip. Blender for Chromebook How would I be able to run Blender on a Chromebook? The Rollapp is a farce that demands money for free software, and the whole reason I didn't buy a windows laptop is because I hate Windows 10, so is there another option? How can I reuse existing materials, objects, etc from an existing .blend? I have created several designs for a particular project and they are related, but I don't want to have to keep recreating any similar elements, such as shared materials or textures.  How can I use the existing data in a new Blender file? Is it possible to run Snow Leopard on a LATE 2011 MacBook Pro? Alt-Tab shows two application switchers on Unity I started to have problems with my Ubuntu application switcher (Alt +  Tab) this morning. When I press Alt +  Tab, not only one, but two application switchers show up. Last night I customized some stuff using the Unity Tweak Tool. I thought I didn't touch the application switcher. So now it looks like this: What is the largest inductance value ever attained(in Henries)? Securely erase hard drive using the Disk Utility I am planning on selling my laptop. So I formatted my disk using the Disk Utility and chose to overwrite the disk with zeroes.  Two questions:  Is this the same as overwriting the disk using dd?  sudo dd if=/dev/zero of=/dev/sda   And is this method secure enough so that buyers can't easily recover the previous data? Or should I take additional measures (like encrypting the disk, destroying the headers, etc.)? Finding a set of continuous functions with a certain property 2 I need help finding the set of continuous functions $f : \Bbb R \to \Bbb R$ such that for all $x \in \Bbb R$, the following integral converges:  $$\int_0^1 \frac {f(x+t) - f(x)} {t^2} \ \mathrm dt$$  I think it might be the set of constant functions but i havent been able to prove it :(   I was thinking that you can use the stone weiestrass theorem considering the set of continuous functions on a closed  interval(non trivial) ,and a subset which contains the set of continuous functions whose integral above diverges in some point in that interval along with  with the set of constant functions. So in order to solve the problem i need only to prove that if two functions do not meet the condition of the problem then their product does not as well .  I hope you can provide some insight and thank you . How do Prestige Classes that advance spellcasting interact with racial spellcasting ability? For example Lets use the Marrutact from Sandstorm, it can cast as a 5th level wizard. if it then takes a prestige class that requires the ability to cast 1st level Arcane spells and advances arcane casting such as Abjurant Champion. assuming it meets all other prerequisites does the Marrutacts spellcasting improve when it takes a level in Abjurant Champion or does it gain no benefit? Parse DateTime with time zone of form PST/CEST/UTC/etc Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$ I want to show that for $\gcd(a,b) = 1$ $a,b \in Z$   $\gcd(a+b, a-b) = 1$ or $\gcd(a+b, a-b) = 2$ holds.      I think the first step should look something like this:      $d = \gcd(a+b, a-b) = \gcd(2a, a-b)$   From here I tried to proceed with two cases. 1: $a-b$ is even, which leads to $\gcd(a+b, a-b) = 2$ 2: $a-b$ is odd, which leads to $\gcd(a+b, a-b) = 1$  My main problem I think is, that I do not know how I should include $\gcd(a,b) = 1$ in the proof.  Any help is appreciated. Thx in advance. Cherio Woltan How do I remove "Ubuntu" in the bios boot menu? (UEFI) I was wondering if there are functions for which $$f'(x) &gt; f(x)$$ for all $x$. Only examples I could think of were $e^x - c$ and simply $- c$ in which $c &gt; 0$. Also, is there any significance in a function that is always less than its derivative?    Edit: Thank you very much for all the replies. It seems almost all functions that apply are exponential by nature...  Are there more examples like - 1/x?  Again are there any applications/physical manifestations of these functions? [for example an object with a velocity that is always greater than its position/acceleration  is always greater than its velocity]