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Let $I = \langle 2\rangle$. Prove $I[x]$ is not a maximal ideal of $\mathbb Z[x]$ even though $I$ is a maximal ideal of $\mathbb Z$.   My professor mentioned that I should try adding something to it to prove that $I[x]$ is not the maximal ideal. I want to assume he meant to add $ \langle 2 \rangle$ to $I[x]$? How do you integrate $e^{x^2}$? I know that $\int{\frac{1}{x}}dx$ is simply $\ln{(x)}+c$ (-which is clearly unrelated to the problem but I just thought I would share anyway) but I am not sure how to approach $e^{x{^2}}$. Perhaps a substitution? Can I charge computers by inducing 5-volt into their USB connectors? Is this possible? I noticed that when my EeePC 900 is off but plugged in charger, there is power coming out of the USB port. Can this be a sustainable way of charging a PC, or a flaw in design? Evaluating a sum involving binomial coefficient in denominator I came across the following sum: $$\sum_{k=0}^{\infty} \frac{(-1)^k}{(2k+1)^2}\frac{4^k}{{2k \choose k}}$$    I thought that this can be evaluated using the expansion of $\dfrac{\sin^{-1}x}{\sqrt{1-x^2}}$ but I couldn't make any use of it. Then I tried to use the following: $$\frac{1}{(2k+1)}\frac{1}{{2k \choose k}}=\frac{\Gamma(k+1)\Gamma(k+1)}{\Gamma(2k+2)}=\int_0^1 x^k(1-x)^k\,dx$$ but this didn't help either and now I am stuck.   Any help is greatly appreciated. Thanks!    EDIT:  The sum originated from the following definite integral:  $$\int_0^{\pi/2}\tan^{-1}(\sin x)\,dx$$ why are the best questions the ones which have been closed? I frequently come across a really useful answer on StackOverflow which has been closed because it doesn't match the Q&amp;A format.  Examples include  ,  ,   ,  and there are others.  Where should this information be exchanged if it's not on stackoverflow?  It seems the moderators are often somewhat overzealous...  ---edit  When I say best, I mean they are informative and useful for someone who's looking for an answer to them.  Even if they do become a bit of a discussion, I value other people's opinions on the relative merits of the different JPA frameworks.  I come here looking to choose one and the answer helps me.  So what if it's not a definitive answer?  ---edit  I don't care how popular a question is, nor how interesting it is.  Users are interested in stuff that's useful to them.  Plenty of those were useful (as judged by the upvotes on the answers: 'This answer is useful'), but closed because they didn't have a definitive answer, as far as I can tell.  ---edit  Seems I'm not the first person to think this: there are various similar questions to mine like this one:   In it the user lists lots of other useful questions which have been closed:                    So isn't there a place on stackoverflow for these questions?  A discussion section, maybe? Was Quirrell the Defense against the Dark Arts teacher for more than one year? It's well seen throughout the series that there is a “curse” on the DADA teacher position, that no one can hold that post for more than a year. But it seems like Quirrell has been around for longer than a year. What's up with that? How to Deserialize XML document How do I Deserialize this XML document:  &lt;?xml version="1.0" encoding="utf-8"?&gt; &lt;Cars&gt;   &lt;Car&gt;     &lt;StockNumber&gt;1020&lt;/StockNumber&gt;     &lt;Make&gt;Nissan&lt;/Make&gt;     &lt;Model&gt;Sentra&lt;/Model&gt;   &lt;/Car&gt;   &lt;Car&gt;     &lt;StockNumber&gt;1010&lt;/StockNumber&gt;     &lt;Make&gt;Toyota&lt;/Make&gt;     &lt;Model&gt;Corolla&lt;/Model&gt;   &lt;/Car&gt;   &lt;Car&gt;     &lt;StockNumber&gt;1111&lt;/StockNumber&gt;     &lt;Make&gt;Honda&lt;/Make&gt;     &lt;Model&gt;Accord&lt;/Model&gt;   &lt;/Car&gt; &lt;/Cars&gt;   I have this:  [Serializable()] public class Car {     [System.Xml.Serialization.XmlElementAttribute("StockNumber")]     public string StockNumber{ get; set; }      [System.Xml.Serialization.XmlElementAttribute("Make")]     public string Make{ get; set; }      [System.Xml.Serialization.XmlElementAttribute("Model")]     public string Model{ get; set; } }   .  [System.Xml.Serialization.XmlRootAttribute("Cars", Namespace = "", IsNullable = false)] public class Cars {     [XmlArrayItem(typeof(Car))]     public Car[] Car { get; set; }  }   .  public class CarSerializer {     public Cars Deserialize()     {         Cars[] cars = null;         string path = HttpContext.Current.ApplicationInstance.Server.MapPath("~/App_Data/") + "cars.xml";          XmlSerializer serializer = new XmlSerializer(typeof(Cars[]));          StreamReader reader = new StreamReader(path);         reader.ReadToEnd();         cars = (Cars[])serializer.Deserialize(reader);         reader.Close();          return cars;     } }   that don't seem to work :-( Counter with 4 flip flops jk synchronous from 3 to 13! I have to create a counter with 4 flip flops jk synchronous. The counter shall count in this order: 3 to 13 and then to 3 to 13 and so on..  I have to use logisim simulator.   Ok. So i think its solved. I realized that the circuit needs to start at 0 ou 1 and stabilize after the 13 and then it goes to 3. Thanks for your help.  Hope this will help for somebody else too.  Thank you all for your help! Setup a decal material in cycles I'm trying to setup a image decal in cycles, and I can't figure how to setup the nodes to work fine. Does anyone know the solution? Deriving ordered statistics minimum cdf Assume ${{X}_{1}}$, ${{X}_{2}}$, ${{X}_{3}}$,...,${{X}_{n}}$  are i.i.d. samples from distribution with density f, and cdf F.  Let V=min( ${{X}_{1}}$, ${{X}_{2}}$, ${{X}_{3}}$,...,${{X}_{n}}$)  To find the minimum $${B}_{v}={\{V\ge{v}\}}=\{{X}_{1}\ge{v}\}\cap\{{X}_{2}\ge{v}\}\cap...\cap\{{X}_{n}\ge{v}\}$$  So, $$P(V\ge{v})=[1-F(v)]^{n}$$  The cdf is  $$F_{v}(V)=1-[1-F(v)]^{n}$$   The density is $${f}_{v}(V)=\frac{d}{dv}[1-F(v)]^{n}=nf(v)[1-F(v)]^{n-1}$$   To find the density, why did we use $[1-F(v)]^{n}$ instead of $1-[1-F(v)]^{n}$, shouldn't we used the cdf to derive the pdf? Your last flag was declined - no it wasn't If $x_1,...,x_n$ are positive real numbers and if $y_k=1/x_k$, prove that $$\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2.$$   I've been learning induction, and I've come across this problem that I really can't even break down and begin to think about. I've been told it has something to do with Cauchy-Schwarz, but I cannot figure out how to apply it. I would appreciate help figuring out how to go about and formulate this proof. Thanks! Redefining \listoffigures and \listoftables as tables Simple Proof by induction: $9$ divides $n^3 + (n+1)^3 + (n+2)^3$ I'm trying to prove using induction that $9$ divides $n^3 + (n+1)^3 + (n+2)^3$ whenever $n$ is a non-negative integer. So far, I have:   Base case: $P(1) = (1) + (8) + (27) = 36, 36$ can be divided by $9$ so the base case is valid Inductive step: let $P(n)$ be the statement $9$ divides $n^3 + (n+1)^3 + (n+2)^3$. Assume $P(k)$ is true, so $9$ divides $k^3 + (k+1)^3 + (k+2)^3$.   And this is where I'm stuck. I'm not sure how to demonstrate that $9$ divides $P(n)$ when $n = k+1$. If someone could step me in the right direction that would be awesome. Thanks! Which registry keys are impacted with Xerox Printer driver installation? I am implementing a driver deployment with Samba.  Every possible model of printer found an easy solution, except for Xerox Workcenter.    After browsing the Internet, I found that Xerox printer driver has to change some registry keys in order to work, keys which are changed by the executable downloadable on the manufacturer website.  Do you know which key are impacted by the Xerox Workcenter GPD driver?  This corresponds to the error message I get while uploading to Samba, which asks the position of a file named as a registry key.  I browse Samba bug tracker and they did not specify which registry key are impacted.  I contacted Xerox itself, but despite that fact that we have a support contract and really a huge number of workstations, it seems that Xerox is not willing to help us. Delete all files except files with the extension pdf in a directory I have a directory that contains the following:  x.pdf y.zip z.mp3 a.pdf   I want to delete all files apart from x.pdf and a.pdf. How do I do this from the terminal? There are no subdirectories so no need for any recursion. I'm setting up a child theme in WordPress and I can't make add_action to be fired within functions.php.  Functions.php is called and I can run code from within. Any idea on what I'm doing wrong?  $debug_msg = "Hi there!";  function test_function() {     error_log($debug_msg, 0);  } add_action('init', 'test_function', 20); Can I use an Android phone as webcam for an Ubuntu device? How do I delete a folder that's in use? Sometimes when I'm working in Windows I'll get this prompt when I try to delete a directory:    Folder In Use The action can't be completed because the folder is open in another program Close the folder and try again.   However, the folder isn't "in use" at all, and I don't have it open. So how can I delete it short of rebooting? Suppose that $y_1(x)$ and $y_2(x)$ are solutions of the differential equation $y''+py'+qy=0$ on $I$. How can I show that if $y_1$ and $y_2$ vanish at the same point then they are not linearly independent?   Here is my attempt to prove the problem. Since $y_1(x)$ and $y_2(x)$ are solutions of the differential equation $y''+py'+qy=0$ on $I$, it is enough for me to show that the Wronskian of $y_1$ and $y_2$ denoted by $W(y_1,y_2)$ is zero. Now since $y_1$ and $y_2$ vanish at the same point say $p$ we have $y_1(p)=0$ and also $y_2(p)=0$.   Solving for $W(y_1,y_2)(p)$ we have: $y_1(p)y_2'(p)-y_2(p)y_1'(p)=0$ since $y_1(p)=0$ and also $y_2(p)=0$.   Am I correct? Thanks