Showing a function is continuous and analytic
Prove the function is continuous, exercise from Conway's "Functions of One Complex Variable I"
Why is the gate charge curve (Miller plateau) of MOSFETs dependent on Vds? What is the meaning of this two letter code in the YouTube logo? I see a new logo with CA at youtube.com. Does anyone know what it means? Why aren't my PIR security lights working through my window? If I want to use objects as the keys for a Dictionary, what methods will I need to override to make them compare in a specific way?  Say I have a a class which has properties:  class Foo {     public string Name { get; set; }     public int FooID { get; set; }      // elided }    And I want to create a:  Dictionary&lt;Foo, List&lt;Stuff&gt;&gt;   I want Foo objects with the same FooID to be considered the same group.  Which methods will I need to override in the Foo class?  To summarize: I want to categorize Stuff objects into lists, grouped by Foo objects. Stuff objects will have a FooID to link them to their category. Rename profile folder on Windows 7/8 Is Let us = Let's? Many times I heard these words interchangeably. I want to know if "Let's" and "Let us" are used for the same meaning.  I think (for me):   "Let us" is word used for requesting. Like Let us do something means requesting to allow us do something. "Let's" is words used for proposing. Like Let's play means proposing people to play. Drag-and-drop functionality no longer working after upgrade to 19.04 After upgrading from 18.04 to 19.04 (with a necessary upgrade to 18.10 between) on a Lenovo Yoga 11e, I can no longer drag and drop anything (ie, files, windows, etc.) with the touchpad.  I can, however, move things around using the touchscreen.  Whenever I attempt to do so with the mouse, though, sometimes it turns into a hand.  Whether or not it turns into the hand or remains a pointer, the icon will not move anymore.  IOW, as soon as I left-click, the pointer freezes in place until I release the touchpad. "going to come down" vs "going to have to come down" What is the difference between the following sentences?        This fence is going to come down.   This fence is going to have to come down.      I have doubt that when you are saying fence is going to have to come down, that is enough to say it right? but why I hear in movies saying fence is going to have to come down, is there a difference between them? Having trouble creating an array of objects In the Final Battle, when you remove doom tokens for rolling successes against an Ancient One do you stop counting successes for that roll? In Arkham Horror you have to roll a cumulative number of successes equal to the number of players to knock off a doom token from the Elder God's health. If you reach the number of players worth of successes do you then stop counting for the player and move on or do you count the extra successes against the next doom token?  We played it so that you kept on adding them but it meant that we turned Nyalothotep into mince meat quite quickly (One Character was blessed had a fight of 6 a shotgun and Fight +1 skill card though) Determine if Term has Grandparent/Great-Grandparent Construction of Dirichlet distribution with Gamma distribution Let $X_1,\dots,X_{k+1}$ be mutually independent random variables, each having a gamma distribution with parameters $\alpha_i,i=1,2,\dots,k+1$ show that $Y_i=\frac{X_i}{X_1+\cdots+X_{k+1}},i=1,\dots,k$, have a joint ditribution as $\text{Dirichlet}(\alpha_1,\alpha_2,\dots,\alpha_k;\alpha_{k+1})$   Joint pdf of $(X_1,\dots,X_{k+1})=\frac{e^{-\sum_{i=1}^{k+1}x_i}x_1^{\alpha_1-1}\dots x_{k+1}^{\alpha_{k+1}-1}}{\Gamma(\alpha_1)\Gamma(\alpha_2)\dots \Gamma(\alpha_{k+1})}$.Then to find joint pdf of $(Y_1,\dots,Y_{k+1})$ I can not find jacobian i.e.$J(\frac{x_1,\dots,x_{k+1}}{y_1,\dots,y_{k+1}})$ Let $a,b,c>0$ such that $a+b+c=3$, find max/min of $\frac1{a^2+1}+\frac1{b^2+1}+\frac1{c^2+1}$ Options for object creation are greyed out I am trying to model a tree. I turned on the Add a sapling add-on in user preferences, however once I want to begin editing the settings, they come up but is grey and doesn't let me click on it.    I have also attached my blend file here: poll() failed, context incorrect? - Example: bpy.ops.view3d.background_image_add() I keep on getting context errors in the Blender Python API.  I don't understand the issue of the context in the API, how do I know which is the correct context?   Thanks! If A and B are correlated with C, why are A and B not necessarily correlated? Let $R$ be a commutative ring with identity and $I$ and $J$ be ideals in $R$.     Show that $R/I\otimes_R R/J\cong R/(I+J)$ as $R$-modules.   This is what I tried.  Define a map $f:R/I\times R/J\to R/(I+J)$ as $f(\bar r, \bar s)=rs+(I+J)$. This is a well-defined bilinear map.  By the universal property of tensor products, we get an $R$-linear map $F:R/I\otimes_R R/J\to R/(I+J)$ which sends $\bar r\otimes \bar s$ to $rs+(I+J)$.  This map is surjective.  So all we need to show is that the kernel of $F$ is $0$.  But I am unable to do this. Calculate Limit 0f nested square roots How to get the current URL within a Django template? How to compare two TeX codes and mark differences with color I would like to find easy tool, which compares two TeX codes and generates a PDF file of the first code, in which the differences from the second code are marked by a given color. I use winedt 7.0 under windows 7.  I just noticed that latexdiff provides what I need. As far as I understand it is included in Miktex. Is there an interface (menu commands) in winedt 7.0, which allow to work with latexdiff ?