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Simultaneously merge multiple data.frames in a list limit of $\lim\limits_{x \to \infty}((x+1)^a - x^a)$ Hello everybody, i couldn't figure out how to demonstrate this equation without L'Hopital i wonder if its possible.   $a \in (0,1)$ $\lim\limits_{x \to \infty}((x+1)^a - x^a) = 0$ I've noticed an interesting phenomenon in the user interfaces of many famous applications, they're moving away from the glossy complex to a more dull and bare minimum design.  Why the sudden change? It also appears that most of these companies have adopted this design around the same time, was that linked to some new study?  Examples: I've got an HP Pavilion Touchsmart notebook that came with Windows 8. I've upgraded to 8.1, and now I want to dual-boot an Ubuntu distribution with Windows 10. When dual-booting with Windows 8.1, the Windows Boot Manager always took priority, even after installing GRUB. What do I need to do to get GRUB to be the default bootloader instead of Windows Boot Manager? C# compiler error: "cannot have instance field initializers in structs" I'm doing some architectural cleanup that involves moving a bunch of classes into different projects and/or namespaces. Currently I'm moving the files by hand, building, and then manually adding using Foo statements as needed to resolve compilation errors. Anyone know of a smarter way of doing this? (We're a CodeRush and Refactor! shop, but I'd be interested to hear if Resharper has support for this) Does "+" use in String concatenation affect efficiency? "Print" and "ui.Label" return different strings in console and in the UI in Google Earth Engine I am working on a variable label in Google Earth Engine and noticed that the label as printed in the console is not the same as the label shown on the map. Why is that? Code below:  var aoi = ee.Geometry.Polygon([[[-106.75701284923326, 42.31332966408458],           [-106.75701284923326, 42.003856624775146],           [-106.31755972423326, 42.06913460511273]]]);  var chirpsSelect = ee.ImageCollection("UCSB-CHG/CHIRPS/DAILY")             .filterDate('1985-01-01','2018-01-01')             .filter(ee.Filter.dayOfYear(3,6))             .filterBounds(aoi)  var chirpsStartImage = ee.String(chirpsSelect.first().get('system:index')) var dateStartString = ((((chirpsStartImage.slice(6,8)).cat('/')).cat(chirpsStartImage.slice(4,6))).cat('/')).cat(chirpsStartImage.slice(2,4))   var sortChirpsSelect = chirpsSelect.sort('system:index',false)  var chirpsEndImage = ee.String(sortChirpsSelect.first().get('system:index')) var dateEndString = ((((chirpsEndImage.slice(6,8)).cat('/')).cat(chirpsEndImage.slice(4,6))).cat('/')).cat(chirpsEndImage.slice(2,4)) var dateTitle = ee.String((dateStartString.cat(' to ')).cat(dateEndString))  print(dateTitle)  var dateLabel = ui.Label({   value: dateTitle })  var panel = ui.Panel() panel.add(dateLabel) Map.add(panel) Every subsequence of $x_n$ has a further subsequence which converges to $x$. Then the sequence $x_n$ converges to $x$. Is the following true? Let $x_n$ be a sequence with the following property: Every subsequence of $x_n$ has a further subsequence which converges to $x$. Then the sequence $x_n$ converges to $x$.  I guess that it is true but I am not sure how to prove this. What are the mechanics by which Time Dilation and Length Contraction occur? What are the mechanics of time dilation and length contraction? Going beyond the mathematical equations involving light and the "speed limit of the universe", what is observed is merely a phenomenon and not a true explanation of why time dilates or length contracts.  It has been proven to work out, but do we know why?  Is it something that happens at a subatomic level? Whenever the Doppler effect is mentioned, it's typically in the context of sound waves or electromagnetic radiation. On the cosmological scale, red-shifting is also important because of the enormous speed of receding galaxies, thanks to the expansion of the universe.   Yet, red-shift is always discussed as the red-shifting of electromagnetic waves. Can gravitational waves be red-shifted? If so, could observations of them be used like red-shifted electromagnetic waves from distant sources are; that is, to figure out how fast an object is receding? Word/phrase for the activity of hiding mistakes What word/phrase can I use to describe the activity of hiding a stupid mistake/incident, such as quickly cleaning up tea spilled by accident before anyone could notice? I need a counsel about my websites' domain.  Let's say I have just bought two domains: xyz.com and xyzphotography.com.  As we can see, the first one is shorter but way less meaningful than the second one. The second one contains a photography keyword but it's longer.  I have only one website which is my photography portfolio. Can you advise me how to set those domains to make it all as SEO-friendly as possible? Which one should be the main one, does the rest should work on their own or have some kind of SEO-friendly redirect to the main domain? How can I achieve more clarity in my photos of the moon? I took this photo of the blood moon this morning and I am finding many of my photos, especially landscape photos, have a significant lack of clarity. I'm not looking for a photo critique because I know this particular photo is crap. I'm looking to identify my source of failure to nail a significantly clear photo.     Setup  Canon EOS 70D with a 100-300 telephoto lens (I'm sorry I don't know the exact model. It's from Canon but not one of their professional quality lenses.)   Aperture: f/5.6 Shutter: 1 sec. ISO: 1000 Focal Length: 300mm Metering mode: Spot White Balance: I manually set the WB to 5500 kelvin, it looked fine in live view. Focus Mode: Manual Drive: 2 sec timer delay   Mounted on a decently stable tripod  Process  I turn on live view, and square up the target in the display. I then set my focal length, focus in using live view, adjust the focus as sharp as possible and take the pic. I've noticed that in this case, the picture was incredibly grainy, which doesn't translate to the final photo, but wonder if it has anything to do with it.  This particular shoot I found it difficult to balance out the variables with a dark sky and a moving moon that starts blurring after 1-2 seconds of exposure, which is why I had the aperture wide open and the ISO cranked up.  I can't tell where I'm failing:  Equipment:  The 70d takes great photos but the telephoto is not great when it's totally zoomed in. My wallet doesn't hold enough cash for a motorized mount to track objects in the sky.  Circumstance: I've seen great photos of the moon with the use of a camera and a tripod, so I know this is possible. Although, I keep seeing pictures of this big gorgeous moon over the landscape, and when I use my wide-angle, the moon shows up as a dot. What the hell are people doing to get the moon so big?  Beginner skill level: I know this is the biggest culprit, but being the beginner, I'm unable to know where to adjust. Using differentiation for computing $\int_{0}^{1}\frac{\arctan(ax)}{x\sqrt{1-x^2}}\,dx$ How can I prove that I can differentiate the integral:  $$ \int_{0}^{1} \frac{\arctan(ax)}{x\sqrt{1-x^2}}\,dx $$  First I have to prove this integral converges. Next I have to prove the integral $$ \int_{0}^{1} f_{a}'(x, a)\,dx $$ converges uniformly.  Then I can differentiate integral with Leibniz's rule.  I tried Weierstrass and Dirichlet's tests. Nothing succeeded.   Thank you for help in advance. It is well known that compactness implies pseudocompactness; this follows from . I know that the converse does not hold, but what is a counterexample?  (A  is a topological space $S = \langle X,{\mathfrak I}\rangle$ such that every continuous function $f:S\to\Bbb R$ has bounded range.) How to pass anonymous types as parameters? In summer, should I close curtains during the day? Asymptotic behavior of a trigonometric series Consider the following series $$S_N = \sum_{k=1}^N \frac{\sin[k\pi/(N+1)]}{k}.$$ What is the asymptotic behavior of this series for $N \to \infty$?  If we replace the sine function with the factor $1$, we get the standard harmonic series which diverges $\sim \ln N$. However, if we replace the sine function with $(-1)^k$, we get a convergent series with the result $\ln 2$. Therefore, I think that $S_N$, defined above, should diverge, but more slowly than the logarithm. Am I correct? Why won't my taskbar display on my secondary monitor? On my secondary monitor (currently using Windows 10), my taskbar will barely show up. I've tried adjusting the resolution to lower ones (it recommends 1920x1080) and it doesn't do much. Is there a way to adjust the taskbar so I can see it?  That is about what I see. I could make it bigger via Snipping Tool and see my entire desktop on the picture but not normally.