I want to determine if the following integral converges $$\intop_{1}^{2}\frac{\sin\left(x\right)}{\log\left(x\right)}dx$$ My intuition tells me it diverges. I thought the way to solve that woudln't be by definition but by finding another function that is smaller than that and use integral comparison test. I also know that $$\lim_{x\rightarrow1}\log=0$$ but I don't see how that helps me
I tried to use the absolute convergence test. $$\int_1^2\left|\frac{\sin{x}}{\log{x}}\right| \, dx&lt;\int_1^2\left|\frac{1}{\log{x}}\right| \, dx$$ but I'm not sure whether $\frac{1}{\log{x}}$ converges or not.  Thanks in advance!
Pseudo-terminal message in script Permissions problems with /var/www/html and my own home directory for a website document root I'm trying to not give 777 permission in my /var/www/html folder, but I want to edit my files without sudo. So I though in create a symlink of a folder in my home directory within /var/www/html. I created it using sudo ln -sT /home/andre/www/moodle/ moodle , and the ls -la output is this:  andre@andre-270E5G:/var/www/html$ ls -la total 8 drwxr-xr-x 2 root root 4096 Mai  4 10:20 . drwxr-xr-x 4 root root 4096 Abr 29 14:29 .. lrwxrwxrwx 1 root root   23 Mai  4 10:20 moodle -&gt; /home/andre/www/moodle/   So, my moodle folder has read, write and execute permissions for everyone, and thats not what I want. I used the command sudo chmod -R 775 moodle/ trying to change it, but it stayed with read, write and execute permissions to all. I tried the same with the moodle folder in /home/andre/www/moodle, but it stayed the same. The output of ls -la in /home/andre/www/ is:  andre@andre-270E5G:~/www$ ls -la total 28 drwxrwxr-x  3 andre andre  4096 Mai  4 10:02 . drwx------ 49 andre andre 20480 Mai  4 10:01 .. drwxrwxr-x 41 andre andre  4096 Mai  4 10:02 moodle   So the folder moodle in /home/andre/www/ has the permissions I want.  As an additional problem, when I access localhost/moodle I get 403 Forbidden error.  What am I doing wrong here? how to solve $\int_{-\infty}^\infty e^{-x^2-x{\tau}} \cdot x\ dx$? How to insert pipe symbol in (La)TeX? How to insert pipe symbol | in TeX (LaTeX)?  I have tried this sample with pdflatex tmp.tex  \documentclass{extarticle} \begin{document} \textpipe \end{document}   And it give undefined control sequence error  This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) restricted \write18 enabled. entering extended mode (./tmp.tex LaTeX2e &lt;2009/09/24&gt; Babel &lt;v3.8l&gt; and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, loaded. (/usr/share/texmf-texlive/tex/latex/extsizes/extarticle.cls Document Class: extarticle 1996/10/08 v1.0 Non Standard LaTeX document class (/usr/share/texmf-texlive/tex/latex/base/size10.clo) (/usr/share/texmf-texlive/tex/latex/base/exscale.sty)) No file tmp.aux. ! Undefined control sequence. l.3 \textpipe I've got a DVD that I've burnt from an MSDN ISO. I'm not entirely sure if its Windows 7 64bit or 32bit.   How can I be sure? How can you tell when a participle is being used as an adjective?  I feel completely lost trying to guess. Just as a completely arbitrary example   For every dedicated scientist patiently recording atmospheric pressure and wind speed while shivering at high altitudes, there is a carnival barker with a bevy of pretty girls willing to dangle from a basket or parachute down to earth. Repeating something with (1/n)th chance of success n times How can you change the href for a hyperlink using jQuery? Generating values from a multivariate Gaussian distribution I am currently trying to simulate values of a $N$-dimensional random variable $X$ that has a multivariate normal distribution with mean vector $\mu = (\mu_1,...,\mu_N)^T$ and covariance matrix $S$.  I am hoping to use a procedure similar to the inverse CDF method, meaning that I want to first generate a $N$-dimensional uniform random variable $U$ and then plug that into the inverse CDF of this distribution, so to generate value $X$.  I am having issues because the procedure is not well documented and there are slight differences between the  and a .  In my case, I am also choosing the parameters of the distribution randomly. In particular, I generate each of the means, $\mu_i$, from a uniform distribution $U(20,40)$. I then build the covariance matrix $S$ using the following procedure:   Create a lower triangular matrix $L$ where $L(i,i) = 1$ for $i=1..N$ and $L(i,j)  = U(-1,1)$ for  $i &lt; j$ Let $S = LL^T$ where $L^T$ denotes the transpose of $L$.   This procedure allows me to ensure that $S$ is symmetric and positive definite. It also provides a lower triangular matrix $L$ so that $S = LL^T$, which I believe is required to generate values from the distribution.  Using the guidelines on Wikipedia, I should be able to generate values of $X$ using a $N$-dimensional uniform as follows:   $X = \mu + L * \Phi^{-1}(U)$   According to the MATLAB function however, this is typically done as:   $X = \mu + L^T * \Phi^{-1}(U)$   Where $\Phi^{-1}$ is the inverse CDF of a $N$-dimensional, separable, normal distribution, and the only difference between both methods is simply whether to use $L$ or $L^T$.  Is MATLAB or Wikipedia the way to go? Or are both wrong? Help with packages in java - import does not work What is a virtual terminal for? Hot and Week tabs not shown to non-logged in users (except on SO) Visiting a SE site without logging in, one can no longer access the tabs Hot and Week (except on StackOverflow). I believe this change hides the feature from those most likely to use it: casual, but repeated, visitors. A number of people visit SE sites such as Travel or Mathematics just to read the content. They have no intention to post, and consequently, no reason to register. It makes little sense to hide the Hot and Week lists from them.   I propose that the tabs  ... Hot | Week | Month should again be made visible to anonymous visitors on SE sites, as they are on StackOverflow. Restore SQL Server 2012 backup to a SQL Server 2008 database? Windows 7 / 8 stop modal dialogue flash on parent focus Is there some setting in Windows where I can change the default behavior that causes the border and title of a modal dialogue box to flash like 6 or 7 times when I click on the parent window?  Simply focusing it would be plenty to let me know what I did was wrong.   I don't feel the need for all the sirens and bull horns and strobe lights to let me know I clicked in the wrong place. \bar vs. \overline - when to use what, semantically? Following the question "" which is simply about the lengths of both, I'd like to know when to use \bar and when to use \overline from a semantically viewpoint.  I always used \bar, because up until now I only had single letter mean values to type. But now I came to a problem where I needed a wider "bar".  Then I just tried  \documentclass{article}  \begin{document}   \[ \bar{a} \overline{a} \]   \[ \bar{abc} \overline{abc} \] \end{document}   where one can see that they also differ in position (\overline is lower), and also in thickness (\overline is thicker).  So, the question here is:  What does \bar represent semantically? And when to choose it over \overline and vice versa? If $A$ and $B$ are square matrices such that $AB = I$, where $I$ is the identity matrix, show that $BA = I$.    I do not understand anything more than the following.   Elementary row operations. Linear dependence. Row reduced forms and their relations with the original matrix.   If the entries of the matrix are not from a mathematical structure which supports commutativity, what can we say about this problem?  P.S.: Please avoid using the transpose and/or inverse of a matrix. A better serial voting trap How can I set cron to run certain commands every one and a half hours? I've posted a lot to StackOverflow, and I've noticed something kind of irritating with the formatting in writing questions and comments. If I need to put something inside a &lt; and a >, without spaces in the middle (like right there), it will think it's code and not show up, like this   (obviously it won't come up what I wrote there, or else this wouldn't be an issue, but if you open up the question to edit you can see what's written there.)  If I want it to show up, right now I have to add an extra set of brackets inside of the originals with a junk variable, like right &lt;here> (again, open in edit window to see).  This is really annoying when trying to show variables like lists that require those brackets, and I feel like the junk variables could confuse people looking at the edits. Is there a way to get around this formatting? Thanks! Is denying "Paradoxical Partitioning" equivalent to accepting the Axiom of Choice? In  (to ) it has been noted:     One more point to make about the paradoxical decomposition to more parts than elements [...]   currently we do not know of any model of +$\lnot$ where such decomposition does not exist.    Namely, as far as we know, in all models where choice fails there is some set which can be partitioned into more parts than elements.   (Just for clarification: From the context of the above references the comparison "more parts than" is obviously meant in terms of the  of the suitable  being strictly larger than the cardinality of the suitable initial set itself.)  Now, I find the negation or denial of such "paradoxial partitioning" interesting; i.e. the statement (proposition, "$\lnot$PP"):  "Each partition of each given set has cardinality less than, or at most equal to, the cardinality of the given set."  And I like to further explore how this suggested "proposition $\lnot$PP" (being considered along with ZF, of course) relates to "the standard set theory including Axiom of Choice", . Therefore  My questions:      Are there any models of ZFC known (or could there be any such models, in principle) in which there is some set which can be partitioned into more parts than elements ?  And:  Are there any models of ZF known (or could there be any such models, in principle) in which there is no set which can be partitioned into more parts than elements, and which is not also a model of ZFC ?  (And just for reference: Is there a conventional or concise way of expressing the suggested "proposition $\lnot$PP" in terms of standard notation, such as used in the sources linked above? Has it perhaps been discussed already, by some other name? ...)