I am returning from US to Bangalore. I was travelling on B1 Visa. While going to US, I was carrying one Laptop from Office. I have ID for this Laptop as well.  In US I have purchased a Laptop ($399) and one Surface Tablet($199). Will I be charged in the customs? If yes, How much?
I am planning to travel to India (COK airport, Kerala) from United States. I want to take my laptop as well as my tablet (iPad). Am I allowed to take both in my backpack with my documents related my work. I think I am allowed to take only one computer as per the rule. Will the customs consider my iPad as a computer?  What all I can take?   One of my friends took 2 laptops (1 work and 1 personal) and had trouble at the airport.  Also I am planning to take some wristwatches (7 of them, each avg price is 45 $). I read in a website that I can take stuff up to max 35000 INR. Is that true? In that case, how will I manage my stuff?
Proof of $\sin nx=2^{n-1}\prod_{k=0}^{n-1} \sin\left( x + \frac{k\pi}{n} \right)$ I have seen this identity on Wolfram mathworld and in a comment to another similar trigonometric proof:    I can't seem to find a proof to this identity online anywhere. What method is used to prove this? Prove $\int_0^{\infty}\! \frac{\mathbb{d}x}{1+x^n}=\frac{\pi}{n \sin\frac{\pi}{n}}$ using real analysis techniques only I have found a proof using complex analysis techniques (contour integral, residue theorem, etc.) that shows $$\int_0^{\infty}\! \frac{\mathbb{d}x}{1+x^n}=\frac{\pi}{n \sin\frac{\pi}{n}}$$ for $n\in \mathbb{N}^+\setminus\{1\}$   I wonder if it is possible by using only real analysis to demonstrate this "innocent" result?  Edit A more general result showing that  $$\int\limits_{0}^{\infty} \frac{x^{a-1}}{1+x^{b}} \ \text{dx} = \frac{\pi}{b \sin(\pi{a}/b)}, \qquad 0 &lt; a &lt;b$$ can be found in How can it be that, if like charges repel, they don't repel themselves? In other words, why don't charges break apart?  About the possible duplicate: I want to know about charges in general, not just that of an electron. My response to :  Thank you very much for the extensive explanation. Unfortunately it's a bit above my level (I'm a first year electrical engineering bachelor student). This is how I understand it: If the charge is the sum of multiple separate charges, there has to be an external force that keeps this charges together. However we most often think of electrons and protons as point charges. In other words, we don't think of them as if they are made up from different (smaller) parts. But the idea of electrons and protons as point charges has its own problems. I didn't know that the electric field has a mass. From the formula, I understand that $m\propto \frac{1}{r}$. This would mean that $m\rightarrow \infty$ as $r \rightarrow 0$ (or $r = 0$), which of course is physically not possible. But there is a way to calculate the radius of an electron based on the mass, the speed of light and the constant of Planck. (Unfortunately I don't know why.) You can get around this by a technique called called renormalization, which causes the integral to converge. Unfortunately, I don't understand the rest of the answer due to my level in physics. Nevertheless I am grateful for you answer. It would be awesome if you could confirm or correct my understanding. In bash, how can I convert a Unicode Codepoint [0-9A-F] into a printable character? I have a list of Unicode codepoints, but I don't know of a "simple" way to convert these hex values into the actual characters they represent...    I've heard that zsh has echo -e '\u0965', but I use bash 4.1.  Is there something as simple as the zsh method, for bash? Can we make the "expanded user card" privilege universal? Pursuant to discussion on the , several have asked how far they'll need to search to determine if a user has expressed their preferred pronouns. This requested feature could create an easy solution for that concern.  On sites where I've reached the  privilege level, users can hover over my picture to see a snippet of my profile:    This is where I've included my preferred pronouns, and where I see many others including them as well.  By making this feature universal, users could quickly and easily check for preferred pronouns without needing to navigate to another page. Can I use the Adwaita theme in Unity without installing GNOME shell? I recently installed Ubuntu 11.10 (new install). I would like to use the Adwaita theme with Unity, but it seems that it is not available in the theme selection dialog. I know I get it there after installing gnome-shell, but is there a way to use Adwaita theme for Unity without installing gnome-shell? I have installed Ubuntu on my D: partition using Wubi. Is there any way in which I can remove my Windows from C: drive and move my existing Ubuntu installation to C: drive and make it a regular install. I know that taking the derivative of position with respect to time defines what we call velocity, but I've never heard of physicist going in the opposite direction with position. Is there any application for the integral of position with respect to time?  Maybe with respect to something else? Unexpected voltage with switch turned off Can anyone explain how one would convert one voltage range to another? I'm going to need to convert a range of -10 to +10 volts into a range of 0 to +5 volts. How would this be accomplished? Thanks!   Let me say  something more. Inside of a torpedo there are gyroscopes. This gyroscope give -10 volts when the torpedo have 180 degrees of deviation to the west and 10 volts when the deviation is to the east. This signal is DC, so i need to change this range a range: 0 to 5 v DC . Thanks Why not use tables for layout in HTML? It seems to be the  that tables should not be used for layout in HTML.   Why?  I have never (or rarely to be honest) seen good arguments for this. The usual answers are:   It's good to But this is a fallacious argument; . I guess it's true that using the table element for layout has little to do with tabular data. So what? Does my boss care? Do my users care?Perhaps me or my fellow developers who have to maintain a web page care... Is a table less maintainable? I think using a table is  than using divs and CSS.By the way... why is using a div or a span good separation of content from layout and a table not? Getting a good layout with only divs often requires a lot of nested divs. Readability of the codeI think it's the other way around. Most people understand HTML, few understand CSS. It's better for SEO not to use tablesWhy? Can anybody show some evidence that it is? Or a statement from Google that tables are discouraged from an SEO perspective? Tables are slower.An extra tbody element has to be inserted. This is peanuts for modern web browsers. Show me some benchmarks where the use of a table significantly slows down a page. A layout overhaul is easier without tables, see .Most web sites that need an upgrade need new content (HTML) as well. Scenarios where a new version of a web site only needs a new CSS file are not very likely. Zen Garden is a nice web site, but a bit theoretical. Not to mention its  of CSS.   I am really interested in good arguments to use divs + CSS instead of tables. I see that one time out of the twenty total tests they run, $p &lt; 0.05$, so they wrongly assume that during one of the twenty tests, the result is significant ($0.05 = 1/20$).      Title: Significant Hover text: "'So, uh, we did the green study again and got no link. It was probably a--' 'RESEARCH CONFLICTED ON GREEN JELLY BEAN/ACNE LINK; MORE STUDY RECOMMENDED!'" How to vertically center content with variable height within a div? OSX Server: should I use Open Directory? When should I use "shall" versus "will"? Which is the correct use of these two words, and in which context should one be used rather than the other? Time Dilation When In Orbit Imagine a space ship orbiting the sun at near relativistic speeds, when compared to Earth (say from the reference frame of the sun) there would be x amount of time dilation.  This would mean people on the ship could live for 100's of Earth years.  My question is what would happen if a second ship flew directly away from the Sun and back (ignoring acceleration) at the same speed the orbiting ship is travelling, would the time dilation for the ship that travels in a straight line be the same as that moving in a circle?  The reason I ask is that I was imagining a scenario where intergalactic travel is possible as time dilation means even a journey of light years only ages the crew a fraction of that time, with space stations orbiting certain star systems at similar speeds so that people that don't work on ships can live a similar length of time. I understand that time dilation is all linked to a certain reference frame but working with a reference frame of the sun what would the time dilation be for the different objects taking different paths but at the same speed relative to the sun? If the ship docked back with the space station would they both say the same amount of time had passed? Reattach to lost X11 session I'm using X11 forwarding over ssh to run Linux apps on my Windows box, and when the network drops it loses everything that was running. Is there anything similar to screen for X11? Shell Script - how to scp into remote server and download files and protect password When you lift a box from the floor, the potential energy changes but kinetic energy does not change. Does it violate conservation of energy? Please try and answer this question. How does TeX actually work?