I would like to know if there is a way to make a http download via batch script just with the standards programs in windows (XP and 7) and without PowerShell.  Please, don't give programs I need to install (unless I can install them via command line and without PowerShell).  Can someone please help me?  Edit: I wanted to know if there is a way with batch script alone, without other types of scripts, I did not see that question but someone marked me as a duplicate...
Without using any non-standard (Windows included) utilities, is it possible to download using the Windows command line?  The preferred version is Windows XP, but it's also interesting to know for newer versions.  To further clarify my question:   It has to be using HTTP The file needs to be saved Standard clean Windows install, no extra tools   So basically, since everybody is screaming , I want simple Wget functionality, without using Wget.
Show rigorously that the sum of integrals of $f$ and of its inverse is $bf(b)-af(a)$ Suppose $f$ is a continuous, strictly increasing function defined on a closed interval $[a,b]$ such that $f^{-1}$ is the inverse function of $f$. Prove that,   $$\int_{a}^bf(x)dx+\int_{f(a)}^{f(b)}f^{-1}(x)dx=bf(b)-af(a)$$   A high school student or a Calculus first year student will simply, possibly, apply change of variable technique, then integration by parts and he/she will arrive at the answer without giving much thought into the process. A smarter student would probably compare the integrals with areas and conclude that the equality is immediate.  However, I am an undergrad student of Analysis and I would want to solve the problem "carefully". That is, I wouldn't want to forget my definitions, and the conditions of each technique. For example, while applying change of variables technique, I cannot apply it blindly; I must be prudent enough to realize that the criterion to apply it includes continuous differentiability of a function. Simply with $f$ continuous, I cannot apply change of variables technique.  Is there any method to solve this problem rigorously? One may apply the techniques of integration (by parts, change of variables, etc.) only after proper justification.  The reason I am not adding any work of mine is simply that I could not proceed even one line since I am not given $f$ is differentiable. However, this seems to hold for non-differentiable functions also.  I would really want some help. Pictorial proofs and/or area arguments are invalid. IllegalArgumentException: Invalid column What is a socket? Change the folder that Windows Explorer starts at In Windows7, when you open the Windows Explorer using the pinned Windows Explorer button on taskbar, it opens WE and points it to My Documents folder.  Is there a way to change this so it doesn't open My Documents, but rather "Computer" just as Windows+E keyboard shortcut does? Automatically set description list `labelwidth` based on widest label? How do I create a description list where the item text is automatically indented to the width of the widest label?  This is the same question as  but I would like the width of the widest label to be automatically calculated.  For example, I'd like the following output:    to be produced by the following input:  \documentclass{article} \usepackage{calc} \usepackage{enumitem} \usepackage{lipsum} \usepackage[margin=1em,papersize={4in,2.2in}]{geometry}  \newenvironment{mydescription}{%   \begin{description}[     leftmargin=!,     labelwidth=\magicgoeshere,     ]% }{%   \end{description}% }  \newcommand{\text}{long long long long long long long long long long   long long long long long long long long long long long long long   long long long long long long long text}  \begin{document} \begin{mydescription} \item[The longest label] text \item[Short] \text \end{mydescription} \hrule \begin{mydescription} \item[Medium label] text \item[Short] \text \end{mydescription} \end{document} Evaluating $\int P(\sin x, \cos x) \text{d}x$ Suppose $\displaystyle P(x,y)$ a polynomial in the variables $x,y$.   For example, $\displaystyle x^4$ or $\displaystyle x^3y^2 + 3xy + 1$.  Is there a general method which allows us to evaluate the indefinite integral     $$ \int P(\sin x, \cos x) \text{d} x$$   What about the case when $\displaystyle P(x,y)$ is a rational function (i.e. a ratio of two polynomials)?   Example of a rational function: $\displaystyle \frac{x^2y + y^3}{x+y}$.    This is being asked in an effort to cut down on duplicates, see here:   and here: Why would perfectly similar data have 0 mutual information? Is a photon "fixed in spacetime"? What is the easiest way to swap occurrences of two strings in Vim? How to handle relative urls correctly with a nginx reverse proxy I want to create this:  Note that wire lay chaotically, so spiral object not the same thing.  There is a cool way to do this task in 3ds max:  Basically he deform straight spline/curve and then bend it couple iterations (over 9000 degrees angle in max).   Blender can't bend that way with simple deform as I know, only up to 360 degree. Is there any other way to make wire wrapping similar to photo? When and how did "momentarily" come to mean "in a moment", rather than "for a moment"? "Momentarily" used to mean "for a moment" only, and not "in a moment". Thus, newscasters could be divided into two clear groups: those who would say "we'll be back momentarily," and those who would not.  This restriction made sense to me, because having both definitions would promote ambiguity if a unique interpretation could not always be derived from the context. But in recent years it seems "momentarily" is regularly, maybe even more often, used to mean "in a moment" by newscasters of every caliber, and in fact this is even shown to be the definition when looked up in most dictionaries.  When did this word's meaning change? How did it come about? I am trying very hard to install Canon LBP2900b Printer in Ubuntu 13.10.  I have searched and googled a lot for the solution over fortnight but none of the site / link gave me the simple solution for me. How can accomplish my goal? I have a skyscraper building but I only want the glass in the texture to be glossy.  How would I accomplish this?    Ok, I have done a test and here are the results.  Here is the original:   here is an adjusted image I occasionally update my kernel from this web site    I have been always downloading 3 deb files for installing  linux header all, linux image and linux headers. I noticed one more deb file recently for 64 bit kernel called Linux-image-extra.  I would like to know what does kernel file Linux-image-extra do and should I also install it? Do I need a transit visa for waiting 23 hours in Dubai airport? I am an Indian citizen living in Ukraine. I will be traveling to India but I need to wait in Dubai airport 23 hours for my next flight to India. I will not be leaving Dubai airport.  So in this case do I need a transit visa? Test the convergence of the series For $a&gt;0$, test the convergence of the infinite series: $$\sum a^{\ln(n)}$$ Which test should be better to use here? I tried the D'Alembert's ratio test. $$\lim_{n\to \infty} {\frac{a^{\ln(n)}}{a^{\ln(n+1)}}}= \lim_{n\to \infty}a^{ln{\frac{n}{n+1}}}=a^0=1$$ So the test failed.  UPDATE: I observed that $${a^{\ln(n)}}=e^{{\ln(a)}{\ln(n)}}={n^{\ln(a)}}={{1\over n^{ln({1\over a})}} }$$Further by test of auxiliary series $$\sum \frac{1}{n^p}$$ we know that criterion for convergence is $p&gt;1$. Here $p=ln({1\over a})$.Hence the series will be convergent when $ln(a)&lt;-1$ i.e. when $0&lt;a&lt;1/e$, since $a&gt;0$ is already given.Finally this solved my question. Why do we notate the greatest common divisor of $a$ and $b$ as $(a,b)$? In my textbook on elementary number theory from a class last year, as well as elsewhere through my academic experience and even posts here, I often see the greatest common divisor notated as $(a,b)$ (where this represents the greatest common divisor of $a,b$).  My question is, why is such an unusual notation used? I say it's unusual (if not a bit absurd), for a couple of reasons:   It is unintuitive. It does not grant the reader an immediate knowledge of what it means. In particular, I can easily see it being misinterpreted as an ordered pair of points, and not as a function (which it basically is and I touch on in a second) or representing a single value. Good notation would be immediately understood, no? One should not struggle with parsing through the context or meaning. A clearer notation is often used, and just three letters away. You could certainly think of $(a,b)$ as an ordered pair, if we consider it a function. I often see the alternate $gcd(a,b)$: a function, which takes in two inputs ($a$ and $b$), and outputs their greatest common divisor (or factor, if you prefer). Merely adding the three letters makes the notation clearer by clarifying it is  a function, and using a relatively well-accepted acronym. (Or, at least, I often hear it abbreviated "g.c.d." in school.)   I've mulled this over for a while and I can't think of much without borrowing inspiration from other "unusual" notations. For example:   Common understanding in context: consider the $\log(x)$ function. Depending on context, without a base stated as seen here, it can be presumed to mean whatever is most "appropriate." It could be base $e$ (common in mathematics), base $10$ (common in engineering), or base $2$ (common in computer science). The ambiguity is essentially resolved by context in other words - personally, not a fan of that (I like the explicit stating of bases for full clarity), but if such a motivation holds elsewhere, it might stand to reason that $(a,b)$ could just be taken as a shorthand and "understood" in the context of number theory to simply be the greatest common divisor. That it is in fact used despite $gcd(a,b)$ being clearer and somewhat common also does seem to suggest this playing a role. Perhaps it just started that way and it kept being used. For example,  (based on a ) regarding how logarithms, roots, and exponentiation can be unintuitive from a notation perspective, and proposes an alternative, easier to understand notation. I haven't been in middle school in nearly a decade, but guessing from discussions online, that obviously hasn't really picked up too much. In that sense, perhaps it's like that for $(a,b)$: like we still notate exponentiation, etc., the same way today despite how counterintuitive it is (at least for students), perhaps it just "stuck" and proliferated?   I wasn't able to easily find any reason why online, and it bugs me a bit, so I ask:     Why do we so unintuitively notate the greatest common divisor of two numbers $a,b$ as $(a,b)$?   I of course recognize that this is somewhat moot in light of how easily it's made clear - as established above, all I have to do is append the front of the parenthetical by $gcd$ or $gcf$ to make it way better. And of course, people do that. But I'm more curious in where this ambiguous former notation arose and, in light of a better notation, why it is still used today. When is a CDATA section necessary within a script tag? Are CDATA tags ever necessary in script tags and if so when?  In other words, when and where is this:  &lt;script type="text/javascript"&gt; //&lt;![CDATA[ ...code... //]]&gt; &lt;/script&gt;   preferable to this:  &lt;script type="text/javascript"&gt; ...code... &lt;/script&gt; "Bring" vs. "take" in American English