How can we say charger's output is 5V and 2.1A without giving resistance?
Choosing power supply, how to get the voltage and current ratings?
Evaluation of $\lim_{n\rightarrow \infty}\frac{n!\cdot e^n}{\sqrt{n}n^n}$ without stirling approximation Evaluation of $\displaystyle \lim_{n\rightarrow \infty}\frac{n!\cdot e^n}{\sqrt{n}\cdot n^n}$   $\bf{My\; Try::}$we can write it as $$l=\lim_{n\rightarrow \infty}\frac{e^n}{\sqrt{n}}\cdot \left(\frac{1}{n}\cdot \frac{2}{n}\cdot \frac{3}{n}\cdots \cdots \frac{n}{n}\right)$$  $$\ln (l) = \lim_{n\rightarrow \infty}\bigg[n-\frac{1}{2}n+\sum^{n}_{r=1}\ln\left(\frac{r}{n}\right)\bigg]$$  Now how can i solve it, Help required, Thanks "Try and" versus "Try to"? Why can this product of rectangular matrices not be the identity matrix? Fast way to come up with solutions to $x(x-1)(x-2)(x-3)=1$? I can solve this equation $x(x-1)(x-2)(x-3)=1$ using the usual method but I am looking for a fast analytical method to solve this. Any hints ? Where does gravitational waves' energy go? Vacuum sealing vs. water displacement method when doing longer sous vide cooking Modernist Cuisine recommends that for longer sous vide cooking (times greater than 36 hours) that bags are vacuum sealed rather than just using the water displacement method to remove the air from a ziploc bag.  What is the reason for this? Will I be losing something essential if I just use a regular ziploc bag without vacuum sealing? In SQL Server, how do I "floor" a DATETIME to the second/minute/hour/day/year?  Let's say that I have a date of 2008-09-17 12:56:53.430, then the output of flooring should be:   Year:  2008-01-01 00:00:00.000 Month: 2008-09-01 00:00:00.000 Day: 2008-09-17 00:00:00.000 Hour: 2008-09-17 12:00:00.000 Minute: 2008-09-17 12:56:00.000 Second: 2008-09-17 12:56:53.000 Can Debian identify rarely used packages? I'd like to find a tool that could tell me which Debian packages on my system have been rarely or never used, perhaps by looking at file lists and access times.  This is to find candidates for deletion from my nearly full hard drive.  I'm not very well informed about the rich ecosystem of desktop GUI tools (I use aptitude); does anyone know if one of those tools, or any other tool, can identify how recently a package has been used? I installed Ubuntu 12.04 a month ago and am using it till now. I failed to notice that all this time there was no sound at all while running Ubuntu, even while playing a game in Wine. The weird thing is that only the startup sound comes when I log in (Indian/African drum tone), then comes the utter silence.  I tested both Digital Output (S/PDIF) and the speakers in the sound settings but can hear nothing.  Any help? How do I remove objects after building them, for example a fence that I placed without taking into account its orientation? I have right clicked on it like you would a structure but nothing happened. I have also tried Shift+Alt+Click and nothing has happened. I couldn't think of any other solutions as this is my first game. Remove a part of a list of names I have some files and each files have distinct name but all of them have the same "-statement" at the end like this:  flower-statement.mp3 leave-statement.mp3  ball-statement.mp3 goal-statement.mp3   So I want to remove this: -statement  Is that possible? Hair particles render not same as 3dView(Eevee) Hair particle renders are not same as in 3dView(Eevee). Hair is using Principle Bsdf shader and  camera is set to Orthographic. Force and turbulence fields are applied to it. How to resolve this? Computer unstable at lower temperatures My computer is playing some strange joke at me, and I'm at a loss.  Everybody knows that hot temperatures causes many components to become unstable and even cause damage. When I built this machine, I was careful to do a bunch of experiments with different airflow configurations, with CPU-and-GPU intensive benchmarks running, and measuring the temperature at different points to find the best configuration.  Generally, the internal temperature of this machine is very close to ambient temperature (with 2 exceptions: the GPU always runs ~10°C above ambient, and the CPU goes to at most ~12°C above ambient when running CPU-intensive applications).  Now comes the problem: at really cold mornings. At cold mornings (~10°C (50°F) or below), the system shows really strange general instability. Beeps from the BIOS, the operating system displays strange messages about memory corruption and PCI devices that failed to initialize, and then, everything hangs. The computer hangs to the point that all USB devices turn of. Hitting the Reset button blanks the screen but the mainboard fails to proceed to the boot.  I never thought that low temperatures could cause computer instability. And 10°C is not that cold, it is still within operating temperatures of all components as far as I checked.  I'm quite sure it is related with the temperature. There were too many cold and warm mornings that demonstrated that the problem only showed in the cold ones. I'm working around this problem by letting the computer sit at the GRUB menu for some 5-10 minutes before letting the OS start, or blowing hot air inside the case if I'm in a hurry.  I don't know what should I approach next to find the source of this problem. Since it is difficult to reproduce (I need a cold morning, and the computer must be cooled down (powered off for many hours)), I need to plan ahead the experiment, since it stabilizes after a few minutes on.  Machine is an ASUS P5VDC-X equipped with Intel P4 64-bit 3GHz, 2GB of DDR2 RAM, a 500W PSU and an nVidia GeForce 9600GT. Everything else was already disconnected/removed before and the problem persisted, so the problem should be in one of these remaining parts.  Any help is appreciated! If you draw two circles that are exactly the same in all aspects (location, size, etc...) except they have different colors, then the "border" of the underlying circle is showing through.  \documentclass[10pt]{book} \usepackage{xcolor} \usepackage{tikz}  \begin{document}  \begin{tikzpicture}     \fill (0,0) circle (0.1);     \fill[color=red] (0,0) circle (0.1);     \fill[color=red] (0.5,0) circle (0.1); \end{tikzpicture} \end{document}   Notice the first circle has a black "edge" around it that looks different than the 2nd circle which doesn't.   The problem is due to the fact that one is anti-aliasing both circles and the edge colors are being blended.   Is there a way to fix this but still have anti-aliasing? (basically render all the objects I need then anti-alias them properly afterwards?)  (I realize TikZ probably can't do anything about this but one doesn't know unless they ask) Adding dynamic graphics to an animation How can I check if my computer's powerful enough to run a certain game? Is there a service that I can use to check if my machine will be able to run a certain game? What is the safest way to move the iTunes Library from one hard drive to another? This may happen later with my iMac, but right now it is happening for my iTunes on PC.  The PC had 60GB of partition to install Windows 7, and right now it is down to about 2GB of free space.  All iTunes purchases, including Music and Movies, are downloaded to  C:\Users\mike\Music\iTunes\iTunes Media\Music  C:\Users\mike\Music\iTunes\iTunes Media\Movies   which will make the C: drive have less and less free space.  (and C: will be more healthy if it has at least a couple of GB of free space).  What is the safest, most proper way to migrate all the media to an external hard drive J: ?  On J:, the path might be:  J:\iTunes\iTunes Media\Music   or  J:\iTunes Media\Music   My guess is that we can change the folder in iTunes, but won't iTunes go to that folder or create it, and find nothing, and index everything wrong?  So, should an exact copy of C:\Users\mike\Music\iTunes\iTunes Media be made as J:\iTunes Media first (probably 30GB of files copying), and then start iTunes and change the preference for the folder to the J: one?  Is there a standard or official method to do this? Complex number identity by trigonometry Show that $\lvert e^{i\theta} - 1\rvert = 2\lvert\sin(\theta/2)\rvert$ by using the geometry of the triangle with vertices 0, 1, and the midpoint of the line joining 0 and $e^{i\theta}$.  I have been able to show this identity through other means, however I am stuck on how to utilize this particular triangle. I have read that a holomorphic function in an open disc has a primitive in that disc. Does this mean that for any holomorphic function $f$ in any open set $U,$ that $f$ has a primitive? I say this because I can take a large enough open disc to cover the open set $U$ and find its primitive there. Is this a correct way of thinking? I have a .NET 2.0 WinForms application with a ToolStrip on my main form. Sometimes, the ToolStrip icons don't respond to the first mouse click, so I have to click the icon twice. It's just a standard ToolStrip with several icons and tooltip texts, I don't do anything special. Is this common?