Figure going too much into right in xelatex, not in latex
wrong positioning of figure with tabular in xelatex
Evaluating the double limit $\lim_{m \to \infty} \lim_{n \to \infty} \cos^{2m}(n! \pi x)$ I have to find out the following limit $$\lim_{m\to\infty}\lim_{n\to\infty}[\cos(n!πx)^{2m}]$$ for $x$ rational and irrational. for $x$ rational $x$ can be written as $\frac{p}{q}$ and as $n!$ will have $q$ as its factor the limit should be equal to 1. the second part of irrational is giving me problems. I first thought that limit should be zero as absolute value of cosine term is less than 1 and power it to infinity you should get $0$. But then I realised that it was wrong. I brought the limit down to this form. $$e^{-\sin^2(n!πx)m}$$ after this I find the question quite ambiguous as they have just said $x$ is irrational. If I take $x$ as $\frac{1}{n!π\sqrt{m}}$ I get the limit as $\frac{1}{e}$ but if I take  $x$ as $\frac{2}{n!π\sqrt{m}}$ I get the limit as $\frac{1}{e^4}$. please help me and tell me where have I gone wrong? How do I time a method's execution in Java? Height/Radius ratio for maximum volume cylinder of given surface area Prove that if $p \equiv 3 \pmod{4}$ then $x^2+y^2 \not \equiv 0 \pmod{p}$ Let $x$ and $y$ be integers not congruent to $0$ modulo $p$ where $p$ is a prime. Prove that if $p \equiv 3 \pmod{4}$ then $x^2+y^2 \not \equiv 0 \pmod{p}$.   I thought about proving this algebraically and by contradiction. So we say $x^2+y^2 = pz$ and have to show this is impossible. Is there a "Places" menu for Ubuntu Unity? Use of Website Category Landing Pages OK, here's the situation: A reasonably simple website with a primary navigation menu including drop-down list of sublevels on hover. Each navigation level may have 3 - 6 sublevels below it, none more important than the other. For example see this mockup:    My question is: What should happen if the user Clicks on one of the primary navigation options (such as 'News') instead of just hovering over and choosing a sublevel?  My instinct tells me that I should allow a click of this navigation option; it's expected user behavior to be able to click navigation options. If clicked then a landing page of some sort will be present listing all the sublevels (latest news, blog posts, case studies'). However there is no content to add to this landing page other than presenting a list of links, which is pretty useless. I could pad it out by adding iconography and descriptions of the sublevels, but that's just content for the sake of it; does 'Latest News' really need a description in order to understand what it is?  If I don't include a landing page then clicking this primary navigation will have to open something but if I open the 'Latest News' page that risks the user not knowing about the other sections of the site.  (The landing page will be useful for breadcrumb navigation too, so I don't really want to do away with it).  Is my thinking that a landing page showing the list of sublevels actually useful even though there is no actual content to display, or is there a better alternative to go with? When a player joins the server, this command block (containing gamemode 2 @a) puts them into gamemode 2/adventure mode. How can I change this so that only non-admin/not "opped" players' gamemode gets changed? $A_n:Y\rightarrow Z$ are operators that strongly converge to $A$. Also, $\|A_n\|_\text {op}\le c$ for $c&gt;0$. Given a compact operator $T:X\rightarrow Y$, I need to show that $A_nT$ converges to $AT$ in operator norm (all spaces in this question are Banach spaces).     I was unable to prove this and I also do not understand why we need to assume that $T$ is compact. Any ideas? How do I get an array of repeated characters from a string using LINQ? How to download all required Ubuntu drivers Is there a package of Ubuntu drivers as driver pack solution? I tried to search for it, but I did not find it. If there is, how can I easily get it? How to enable Hyper-V in Windows 8 I've got a Windows 8 (not .1, not Pro; OEM with a Lenovo Z580 laptop), which I want to use for WP8 development.  I've read  and , and a few more articles.  I have enabled in BIOS what looks like it has to do with hardware virtualisation - "Intel Virtual Technology" (is this VMX?). No signs of EPT or XD.  I've got the four Hyper-V items in the enumeration that msinfo32 shows.  However, in the 'Control Panel/Programs and Features/Turn on|off windows features' list, I don't have Hyper-V.  Is this available at all on my machine, and if not what can I do to get it working?  Thanks in advance. Add leading zeroes to number in Java? Is there a better way of getting this result? This function fails if num has more digits than digits, and I feel like it should be in the library somewhere (like Integer.toString(x,"%3d") or something)  static String intToString(int num, int digits) {     StringBuffer s = new StringBuffer(digits);     int zeroes = digits - (int) (Math.log(num) / Math.log(10)) - 1;      for (int i = 0; i &lt; zeroes; i++) {         s.append(0);     }     return s.append(num).toString(); } How do I calculate the closest power of 2 or 10 a number is? Abount linear functional: If $T(B)$ is bounded, is $T$ bounded? Let $H$ be a infinite dimensional Hilbert space and let $B$ be a basis of $H$ that $H=\overline{span(B)}$  moreover, let $T : H \rightarrow K$ be a linear functional   If $T(B)$ is bounded, is $T$ bounded? I've got a small piece of code that is parsing an index value to determine a cell input into Excel.  It's got me thinking...  What's the difference between   xlsSheet.Write("C" + rowIndex.ToString(), null, title);   and  xlsSheet.Write(string.Format("C{0}", rowIndex), null, title);   Is one "better" than the other? And why? LIGO has announced the detection of gravitational waves on 11 Feb, 2016. I was wondering why the detection of gravitational waves was so significant?   I know it is another confirmation of general relativity (GR), but I thought we had already confirmed GR beyond much doubt. What extra stuff would finding gravitational waves teach us? Is the detection of gravitational waves significant in and of itself, or is there data which can be extracted from the waves which will be more useful? Atmospheric pressure In FBD doubt Let us say I have a beaker floating in a water tank. Suddenly I put some water in the beaker also. The figure here shows the exact situation   Now I want to draw the FBD of the beaker. I am somehow confused with the role of the atmospheric pressure in drawing the FBD. I thought of two ways of drawing this and I am just unable to figure out which one is right.    Here since the beaker is floating an $F_{buoyant}$ is there in the upward direction which the net mass (beaker+water in beaker) would put its weight downward.  But while solving one question I came to know that total force that a liquid exerts on the bottom of the container is $P_0+m_{liquid}g$ ($P_0$ is the atmospheric pressure). So should the downward force on the beaker be $(M_{beaker}+M_{water in beaker})g+P_0 S$ (S being the base area of the beaker) as in the second diagram down here.    Here the $P_0S$ due to atmospher on the tube gets cancelled by the $P_0S$ exerted by the water in tank on the tube. But what about the $P_0S$ from the water present in the tube? Do the FBD's apply like the one in the new image? Volume of the torus with an integral I haven't seen this behavior out in the wild much, but it happened again recently and I was wondering if a flag could be automatically raised when this happens:   User posts answer Answer is down voted User deletes answer User posts exact same text as a new answer User effectively ditched down votes   Got down voted again? Wash, rinse and repeat. Profit (perhaps after modifying the post, which is what you should have done to begin with)    I feel that this should raise a duplicate content flag, with slightly stronger wording. Would this be possible to implement? Or, perhaps, don't let users post new answers if they have a deleted answer to a question. Rather, force them to edit and restore the deleted answer instead, unless locked by a moderator.  I do have a link, but I don't want a lot of people to descend on it and create an even bigger disruption. It happened exactly as I described. Why does Hermione say she hadn't used a memory charm before? After the wedding, Hermione has to use a memory charm on two Death Eaters, where she states that she has never done it before, but she knows the theory. However, she states that before she left on her adventure, she made her parents forget her, and move to Australia. Is this a contradiction, or is there an explanation?