Solve the following integration
Integral $\int\!\sqrt{\cot x}\,dx $
Mboxcox, interpreting difficult regressions Mboxcox in Stata suggests transforming my variables using a power of 0.1 for the independent variable, and 0.4 for the dependent variable.  I have run the model, and it fixes problems associated with the assumptions of OLS. But certainly, it complicates matters in terms of interpretations.  Please outline possible interpretations and solutions.  Dependent variable is in millions of dollars, and independent variables are number of years.  and a number of dummies which do not require transformation. Prove $\csc(x)=\sum_{k=-\infty}^{\infty}\frac{(-1)^k}{x+k\pi}$ grep a file, but show several surrounding lines? If $X$ is measurable space, $f : X\to [-\infty,+\infty]$, function such that $f^{-1}([-\infty,r))$ measurable for all rational numbers $r$,prove than $f$ is measurable  I know that $f$ is measurable iff set $\{x\in X : f(x)&lt;a\}$ is measurable for all $a\in \mathbb{R}$ but for $a\in\mathbb{Q}$ I don't know how to proceed. Should there be a comma in 'a 30-day, money-back guarantee'? How to change file encoding in NetBeans? Why won't my follower follow me after the "A Night to Remember" quest line? At the end of the "A Night to Remember" quest line, my follower came with me when I was teleported to the Misty Grove. Once there, I told my follower to wait.  Now, when I was teleported back to the real world, my follower's not with me: presumably because he's still waiting at the Misty Grove. I've waited for some time and still he hasn't come back.  How can I get my follower back? In C++, sizeof('a') == sizeof(char) == 1. This makes intuitive sense, since 'a' is a character literal, and sizeof(char) == 1 as defined by the standard.  In C however, sizeof('a') == sizeof(int). That is, it appears that C character literals are actually integers. Does anyone know why? I can find plenty of mentions of this C quirk but no explanation for why it exists. I have been struggling for one hour with this simple problem (QGIS 1.8.0-Lisboa, Windows 7) :  I have a raster layer. I would like to display the label and not only the band value when I use the Identify Features button. Is it possible? I'm trying to run the remove_doubles edit command on multiple selected objects. This is kinda what I got so far...  import bpy   class remDoubles(bpy.types.Operator):     """Remove Doubles on multiple objects"""     bl_label = "Remove Multiple Doubles"     bl_idname = "object.remove_doubles_multi"     bl_options = {'REGISTER', 'UNDO'}      @classmethod     def poll(cls, context):         return len(context.selected_objects) &gt; 0      def execute(self, context):          scene = bpy.context.scene         sel = context.selected_objects          for obj in sel:             scene.objects.active = obj              #do something here             print(obj.name)             bpy.ops.mesh.remove_doubles()          return {"FINISHED"}  myobject = remDoubles()  myobject.execute()   My knowledge about classes isn't too great, please help.  My code needs some work, it just errors out giving a  'TypeError: bpy_struct.new(type): expected a single argument'  But what i intend doing is run through each object applying the remove doubles command for each. How to convert a list of string to a list of int Is there a term for the moment when a lot of users visit/log onto your website at the same time? Is there a term for the moment when a lot of users visit/log onto your website at the same time? If I live in the US, for example, where current interest rates are practically nil, how can I take advantage of the fact that ? How many switches can be stacked/interconnected? Tile Edge Challenge I've been having a problem with these problems for a week now so I thought I'd post it on MSE. Read the text below. . I've also typed it up:  Annabel made a shape by placing identical square tiles in a frame as shown in the diagram above. The tiles are arranged in columns. Each column touches the base but no columns touch the side or top. There are no empty gaps between columns. The frame can be enlarged as needed.  These are the questions. I've also typed them up.    A. Show that it is possible to arrange $7$ tiles so that the ant walks $8,9,10,11,12,13,14,15$ tile edges.   B. Show 6 ways of arranging 7 tiles so that the ant walks a total of 9 tile edges.  C. Show it is possible to arrange 49 tiles so that the ant walks a total of less than 21 tile edges.  D. Show four arrangements of 137 tiles, each arrangement with a different maximum height, so that the ant walks a total of 34 tile edges.  For question $a$, is there a formula relating the number of tile edges exposed to the number of tiles. These are my answers for $a$    For the above picture, it's the left hand side which has the $a$ answers.  However, I'm having a bit of trouble with $b$. I've already got four answers down but where are the other two. My four current answers are in the right hand side of the last image. Also, I'll also appreciate a formula to show the relationship.  I'm also having trouble with $c$. I found out that you get 21 tile edges exposes when you make a $7*7$ square but the answer is asking for less than 21. Can anyone help me. Also, as in the previous questions, a formula to show the relationships would be great.  And for $d$, I am totally lost. I have no idea where to start, and I certainly can't find out four arrangements. So can anyone help me? And as always, a formula is nice  P.S. Please explain this in an understandable formula, as I'm only a Year 7 with the ability to understand linear algebra and parts of quadratics and trigonometry. Also, sorry about the poor imaging. Prove or the disprove the existence of a limit of integrals Let $A \subset \mathbb{R}^2$ be the annulus defined, in polar coordinates, as  $$ A = \{ (r, \theta) \in [0, \infty) \times [0, 2\pi) : 2 \leq r \leq 3 \} \, .$$ Let $F: A \to A$, $F:(r, \theta) \mapsto (r, r \theta \text{ (mod } 2\pi))$. Let $g : A \to \mathbb{R}$ be a continuous function. Discuss the existence of the limit $$ \lim_{n \to \infty} \int_A g \circ F^{(n)}(x) \, \text{d}x \, ,$$ where $F^{(n)} = F \circ F \circ \dots \circ F$ denotes the composition of $F$ with itself $n$ times.  I cannot find a way to attack this problem. Here's what I tried: if $g \circ F^{(n)}$ converged, I think we could take the limit under the integral sign. So I tried to show the convergence of $F^{(n)}$. If it converged, then the limit function must send every point to a fixed point of $F$. So I determined the fixed points of $F$. But I don't think $F^{(n)}$ converges. How to rename multiple files by removing the extension? Body Diode of a MOSFET So for some MOSFETs, specially with Power MOSFETs, the body diode is a flyback diode that (as far as aI can tell) can be conveniently added to the MOSFET's bulk as there already PN junctions (correct me if I'm wrong).  I've looked at the datasheet of a Power P-MOSFET and it has parameters like "Internal Source Inductance" and "Internal Drain Inductance". So, is the build up of reverse voltage on the source and drain sides, when said MOSFET is suddenly turned off, a behavior intrinsic to (at least some) MOSFETs? Or are these from the rest of the circuit, say inductive loads? How do I tell what version and edition of Windows is on the filesystem? I have a large dictionary file with 300,000+ words in it and I'm trying to find all words with the vowels aeiou in that order and have only exactly 5 vowels. My current attempt does not seem to be working and for the life of me I don't understand why.  less mywords | grep -iE [^aeiou]*a[^aeiou]*e[^aeiou]*i[^aeiou]*o[^aeiou]*u[^aeiou]*   I think it get's all the words I'm looking for but there are a few words that pop up which I can not get rid of.  abstemiousnesses ultraserious   There are a few other but they are in the same vein. Curiously, even if I add something like [^u]* to the front ultraserious keeping popping back up! Any solution would be fine however I would like it restricted to grep as we've been told it can be done using only grep.