We have $(1+\frac{c}{n})^n \to e^c$ as $n \to \infty$. Why does a term in $o(\frac{1}{n})$ does not change this asymptotic?
Why is it that   $$\lim_{n \rightarrow +\infty} \left( 1 + \frac{\lambda}{n}+ o \left( \frac{1}{n} \right) \right)^n = e^{\lambda}$$  I once remembered the justification for "ignoring" the $o(1/n)$ but can't recall it again.
Is there evidence of dark matter in our galaxy? Is there evidence of dark matter in our galaxy?  How can we measure this, say, how many percent of the center of our galaxy is dark matter?  I did not find the answer in the question Any ideas how to display a PDF file in a WPF Windows Application?     I am using the following code to run the browser but the Browser.Navigate method does not do anything!  WebBrowser browser = new WebBrowser(); browser.Navigate("http://www.google.com"); this.AddChild(browser); // this is the System.Windows.Window Get bytes from std::string in C++ I'm working in a C++ unmanaged project.  I need to know how can I take a string like this "some data to encrypt" and get a byte[] array which I'm gonna use as the source for Encrypt.  In C# I do    for (int i = 0; i &lt; text.Length; i++)     buffer[i] = (byte)text[i];   What I need to know is how to do the same but using unmanaged C++.  Thanks! Is there a difference between a LED Backlit and LED HD  Display on laptop monitor? or are they the same that is good for the eyes How to reinstall kernels after accidental deletion with a separate boot partition and an encrypted LVM volume? My installation is a Ubuntu 12.04 64 bits (Classic "legacy" MBR - No  EFI/UEFI here) with two partition :   A separate boot partition An encrypted LUKS volume that contains the system Logical Volumes   I seems I accidentaly deleted all the current kernel files with:  sudo apt-get purge 'linux-image-3.8*'    I applied the updates with Ubuntu Software Update, rebooted and then: Ubuntu can't boot.  I tried to boot on a live DVD with a 14.04.1 Ubuntu and can still see my partitions (described later):  /dev/sda1 (boot) /dev/sda2 (Encrypted volume) /dev/sda5 (Logical Volume container)  What are the steps to recover/reinstall the kernel files and dependencies in order to cleanly reboot my installed system?  Thanks in advance I wrote a script to create a big number of heat maps for a given scenario. I would like to save the result of every heat map as an PNG image. I have figured it out doing it with simple Map Rendering but the quality of the result is too low. Furthermore I would like to export to OpenLayers using the same code, which does not seem to be possible with simple rendering.   Now I am trying to do it with QgsComposition instead. Manually in the Map Composer you can just set the paper color to transparent and disable the background of the map canvas.   This is the code that I have so far. I just cannot figure out why it is not working. The result png-file always has a white opaque background.   My OS is Windows 7 and I'm using QGIS 2.6 Brighton.  I hope someone can help me out here.  # PARAMETERS mainPath = 'path/to/folder/' filename = 'filename' imageType = "png" imageWidth_mm = 400 imageHeight_mm = 160 dpi = 300  mapRenderer = iface.mapCanvas().mapRenderer()  c = QgsComposition(mapRenderer) c.setPlotStyle(QgsComposition.Print)  c.setPaperSize(400, 160)  x, y = 0, 0 w, h = c.paperWidth(), c.paperHeight() composerMap = QgsComposerMap(c, x ,y, w, h) c.addItem(composerMap)  # get all items and disable the backgrounds itemList = c.items() c.removeItem(itemList[2]) c.removeItem(itemList[2]) itemList[2].setBackgroundEnabled(False) itemList[3].setBackgroundEnabled(False) # add them to the composition c.addItem(itemList[2]) c.addItem(itemList[3])  c.refreshItems() c.refreshDataDefinedProperty(QgsComposerObject.AllProperties)  c.setPrintResolution(dpi) dpmm = dpi / 25.4 width = int(dpmm * c.paperWidth()) height = int(dpmm * c.paperHeight())  # create output image and initialize it # image = QImage(QSize(width, height), QImage.Format_ARGB32) image = QImage(QSize(width, height), QImage.Format_ARGB32_Premultiplied) image.setDotsPerMeterX(dpmm * 1000) image.setDotsPerMeterY(dpmm * 1000) #image.fill(0)  imagePainter = QPainter(image)  # This part does not seem to have any effect #brush = QBrush(Qt.BrushStyle(0)) # transparent brush # #imagePainter.setBackgroundMode(0) #c.setBackgroundBrush(brush)  c.renderPage( imagePainter, 0 ) imagePainter.end()   imageFilename =  mainPath + filename + '.' + imageType image.save(imageFilename, imageType) print 'image saved' print 'done' How to include a document into another document? I've always wondered how to write the "A ? B : C" syntax in a C++ compatible language.  I think it works something like: (Pseudo code)  If A &gt; B    C = A Else    C = B   Will any veteran C++ programmer please help me out? I have a dataframe with many observations and many variables. Some of them are categorical (unordered) and the others are numerical.  I'm looking for associations between these variables. I've been able to compute correlation for numerical variables (Spearman's correlation) but :   I don't know how to measure correlation between unordered categorical variables. I don't know how to measure correlation between unordered categorical variables and numerical variables.   Does anyone know how this could be done? If so, are there R functions implementing these methods? What is the /boot partition really for? I'm reading a relatively old text on Linux partitions and file systems (the LPIC 1 Certification Bible). It says:     Some versions of the Linux boot loaders cannot access a kernel that is   outside the first 1024 cylinders on a disk. By putting the /boot   partition at the beginning of the drive you can be assured of not   having a problem when accessing the kernel at boot. This problem shows   itself most often in cases of dual booting Linux along with another   operating system that is on the first partition.   Why would a boot loader have "no access to the kernel outside the first 1024 cylinders on a disk"?  Also, what does "putting the /boot partition at the beginning of the drive" mean? I'm planning to visit a summer school in the Schengen zone. What kind of visa should I apply for? I will be attending a summer school which will last 10 days.  I want to know: for applying for a Schengen visa, is the purpose of my trip considered as touristic or study? What is the equivalent of Windows System Properties or Device Manager? I am new to Ubuntu. In Windows, if I want to know my system properties/configuration, I can see it by going to Control Panel and clicking on the System icon. I can also get a detailed list of the hardware detected/installed by going to the Device Manager.  What are the equivalents of these features in Ubuntu, where a user can see his or her system properties and hardware configuration, like RAM, CPU/processor, hard disk capacity, etc.?    Example of Windows System Properties: Example where Hamiltonian $H \neq T+V=E$, but $E=T+V$ is conserved I'm looking for an example of a Hamiltonian $H$, where $H\neq T+V$, but the total energy in the system, $E=T+V$, is still conserved.   While I'm at it, I might as well add that I'd be most interested in an example from a classical field theory. Furthermore, I am looking for a nontrivial example, e.g. where $H$ doesn't just differ from $E$ by some gradient function that integrates to 0 in the action.   In particular, I am trying to get a better understanding of the physical implications of $H$ being conserved when nontrivial variables are used, i.e. physically, what does $H$ this correspond to. Conversely, can one have a system where $E = H$ in one frame, and is conserved, while in another frame $E'\neq H'$, and $H'$ is conserved while $E'$ is not? "Dare speak" vs. "dare to speak" vs "dares to speak" Which is the most appropriate improvement in the following     I am surprised that he dares speak in such a tone to his father.     a) he dares to speak b) he dare to speak c) he dare speak    I think the answer should be 'c' but the book says 'a'. Prove the following $A \setminus (B\setminus C) = (A\setminus B)\cap (A \cup C)$ I want to prove the following so I decide to rewrite the RHS  $$A \setminus (B\setminus C) = (A\setminus B)\cap (A \cup C)$$ $$ A\setminus(B\setminus C) = A\setminus (B \cap C^c) = A\cap (B\cap C^c)^c = A\cap(B^c\cup C) = (A\cap B^c)\cup(A\cap C) $$ there is way that $(A\cap B^c)\cup(A\cap C)\rightarrow (A\setminus B)\cup(A\cap C) = (A\setminus B)\cap (A \cup C)$?  thanks. EDIT  LHS: $$x\in A \vee x\in A\cap C \rightarrow x\in A \wedge x\in C$$ RHS: $$x\in A \wedge x\in A\cup C \rightarrow x\in A \vee x\in C$$  how it can help me? I would like to see my review audit history Confession: I have been suspended a couple times from reviewing activities.  Partial Redemption: I have become better and better at passing audits.   I'd like to see my recent and distant history with audits.  Even better, I'd like to see my history with the various types of audits.    I'm not sure this has much value beyond self-reflection and self-analysis. I'd like to see if there are patterns to when I was more likely to fail (do I get sloppy after 10 or 20?), or if there are certain types of reviews at which I struggle more (e.g., suggested edit vs close question).  I suspect that if I reviewed my history and revisited audits I failed, I could create rules and rhythms for myself to become a better reviewer. Allow a user to read some other users' home directories Can Mage Hand be used in combat to grab something from an opponent?  For example, one could grab a bow out of their hands or the arrows from a quiver, or try to push them out of a tree, etc.  Mage Hand can carry up to 10 pounds, but what is its ability to interact in situations like these? Custom ordering of duplicate targets is not necessarily honored on mobile apps Stop execution of Javascript function (client side) or tweak it