Test if a not class member function exists (SFINAE)
Templated check for the existence of a class member function?
Can we use "there is" for plural nouns? How do I apply a gradient across multiple objects in Illustrator? I have two separate objects that I have applied gradient fill to.  The gradient fill seems to only apply to the objects as individuals. I tried grouping the shapes, but that doesn't seem to change the gradient.    How do I get one gradient to cover all my shapes? Prevent VLC from starting a new instance every time a media file is opened How to disable requiretty for a single command in sudoers? I want to disable requiretty so that I can sudo within scripts, but I'd rather only disable it for a single command rather than everything. Is that possible within the sudoers config? Why do many anime not follow the manga? Why are they usually made shorter? Many anime do not follow the manga history and are made shorter. However there are a few that do follow it or try to finish the history with the manga like the big three (Naruto, Bleach, One Piece), Death Note, and FMA Brotherhood. But others finish the anime without the real ending like FMA, Ouran High School, Pandora Hearts, Tsubasa Reservoir Chronicle. Why is this so? Is it because of the high cost? Or the lack of popularity? Find the limit of $\frac{n^{x}}{(1 + x)^{n}}$ Let $x&gt;0$. Find $$\lim_{n\to\infty}\frac{n^{x}}{(1 + x)^{n}}.$$   What I was thinking involved an inequality, by reason of considering the fact that  $$(1 + x)^{n} &gt; C(n, k) x^{k}$$ for some $k$ such that $n&gt;k$. Expanding the binomial coefficient and taking the $n$ common from each bracket, we have something like $$(1 + x)^{n} &gt; C(n, k) x^{n} &gt; \frac {x^{k}n^{k}}{k! 2^{k}}.$$ But now, I am totally clueless. By intuition, I know that the limit has to be zero, so I just want to prove using the concept of inequalities that what I thought was the right approach (being the sandwich theorem). Any help would be appreciated! Is Gauss's law wrong, or is it possible that $\int_s{\vec E} \cdot d\vec{s}=0$ does not imply $\vec E = 0$? This is a question from David J Griffith's Introduction to Electrodynamics.      A specified charge density $\sigma(\theta)=k\cos(\theta) $ is glued over the surface of a spherical shell of radius $R$. Find the resulting potential inside and outside the sphere.   The question was solved using legendre polynomials and the final answer for potential inside the sphere was : $V(r,\theta) = \frac{kr}{3\epsilon_0}cos\theta$  This final answer is confusing because The Electric field inside the sphere is coming out to be dependent on $r$ and $\theta$ whereas electric field inside a shell, no matter what the charge distribution is outside, is $zero$ from gauss's law.      my doubts:         why is the electric field inside non zero?    Can gauss's law explain this, or does it fail here?      Since solving using ordinary surface integral gave me the same result and since the. divergence inside the shell is $zero$, I concluded that legendre polynomials and gauss's law in differential form are correct. So the problem should be with the integral form of gauss's law : $\int_s{\vec E}.d\vec{s} = \frac{q}{\epsilon_0}$  The answer I got for this doubt is that  "since the charges are glued to the surface, and not evenly distributed, electric field inside need not be zero. "     This is not convincing because proof of gauss's law does not expect the charges to be free to move. presence of an exrernal force that would hold the charges in place does not change the theorem. That is    Say only a single charge $q_i$ is present outside      then $\int_s{\vec E_i}.d\vec{s} = \frac{q_{inside}}{\epsilon_0}=0$      Now if there are more charges, following any distribution, net electric field $\vec E = \vec E_1 + \vec E_2+\vec E_3+...$       So the net flux,       $\int_s{\vec E}.d\vec{s} = \int_s{\vec E_1}.d\vec{s}+\int_s{\vec E_2}.d\vec{s}+\int_s{\vec E_3}.d\vec{s}+. . .=0$   Or is it possible that $\int_s{\vec E}.d\vec{s}=0$ does not imply $\vec E = 0$? How to download all OpenStreetMap highways in a large area? I need to download all highways as line features from OpenStreetMap in a large area (about 10.000km²). Therefore I wanted to use overpass-turbo with the following statement in the wizard:   highway=*   in my chosen bounding box.  Unfortunately it looks like my bounding box is too big, because I get the error:   runtime error: Query run out of memory using about 2048 MB of RAM.   Do I have to change my overpass turbo query or is it not possible to download large datasets in overpass turbo? Which alternative method could I use to download all highways as line features in a larger region. I need to have all attributes, like the type of the highway, "foot=yes/no/...", "access="yes/no/....", etc. and if I use something like geofabrik, these attributes do not appear. What are tag synonyms? How can tag synonyms be distinguished from "real" tags? How are new tag synonyms created? Who can create tag synonyms? How can I delete/reverse/undo bad tag synonyms? What are merged tags? What is a "slug" in Django? These days, the standard way to present differential calculus is by introducing the Cauchy-Weierstrass definition of the limit. One then defines the derivative as a limit, proves results like the Leibniz and chain rules, and uses this machinery to differentiate some simple functions such as polynomials. The purpose of my question is to see what creative alternatives people can describe to this approach. The nature of the question is that there is not going to be a single best answer. I have several methods that I've collected which I'll put in as answers to my own question.  It's not reasonable to expect answers to include an entire introductory textbook treatment of differentiation, nor would anyone want to read answers that were that lengthy. A sketch is fine. Lack of rigor is fine. Well known notation and terminology can be assumed. It would be nice to develop things to the point where one can differentiate a polynomial, since that would help to illustrate how your method works and demonstrate that it's usable. For this purpose, it suffices to prove that if $n&gt;0$ is an integer, the derivative of $x^n$ equals $0$ at $0$ and equals $n$ at $1$; the result at other nonzero values of $x$ follows by scaling. Doing this for $n=2$ is fine if the generalization to $n&gt;2$ is obvious. Form of the Classical EM Lagrangian So I know that for an electromagnetic field in a vacuum the Lagrangian is $$\mathcal L=-\frac 1 4 F^{\mu\nu} F_{\mu\nu},$$ the standard model tells me this. What I want to know is if there is an elementary argument (based on symmetry perhaps) as to why it has this form. I have done some searching/reading on this, but have only ever found authors jumping straight to the expression and sometimes saying something to the effect that it is the "simplest possible". Using "align" instead of "array" in an array of equations Question regarding use of low voltage high current outputs I see every day high voltage, high current; high voltage, low current. I rarely see low voltage, high current; why?  I know that I can take a high voltage, high current signal, send it through a step-down transformer and theoretically get a low voltage high current (with the same power output, of course), but I never see this done.  Can someone give me a reason as to why I wouldn't want a low-voltage high-current scenario? How did half of Darth Maul survive? Prove the summation:  $$\sum_{i=1}^n i! \cdot i = (n+1)! - 1$$ using induction.   base case:  $n=1$: \begin{align*} \sum_{i=1}^1 i! \cdot i &amp;= (1+1)! - 1 \\ 1 &amp;= 2 - 1 \\ 1 &amp;= 1 \end{align*}   This is a question from my test review packet, currently have the base case completed and I am a bit lost on where to go from there. Any help/hints are appreciated. I have complicated math expression:    Vertical spacing between text and fraction line is too small. I tried to define new \frac command (with amsmath package) with adjustable vertical spaces. As you can see, the result is not satisfying:    \documentclass[a4paper,fleqn,leqno]{article} \usepackage{polyglossia} \usepackage{color,pifont,fontspec} \usepackage[top=2.54cm,bottom=2.54cm,left=2.54cm,right=2.54cm]{geometry} \usepackage{tikz,tikz-3dplot,graphicx} \usepackage{mathtools,breqn,amsmath} \usepackage[fontsize=12]{scrextend} \usepackage{array,multirow} \usepackage{pgfplots} \DeclareMathSizes{12}{14}{14}{10} \newcommand{\myfrac}[3][0pt]{\genfrac{}{}{}{}{\raisebox{#1}{$#2$}}{\raisebox{-#1}{$#3$}}} \begin{document} \begin{dmath*}[breakdepth={0},style={\mathindent=0pt},spread={10pt}] {n=\myfrac[3pt]{\myfrac[3pt]{0,0625N+0,0215}{2}-0,043}{\myfrac[3pt]{\myfrac[3pt]{\scriptstyle 0,0625N+0,0215}{\scriptstyle 2}-0,043}{\myfrac[3pt]{\scriptstyle N}{\scriptstyle 2}-1}+0,0215}} \end{dmath*} \end{document}   How can I enlarge verticall spacing in whole fraction? How do you access the Shrine of Winter? In Dark Souls 2 there is a 'Shrine of Winter' near Sinners Rise. When you approach the shrine it will not let you open the door and a message pops up that says      Seek Mightier Souls   What does this mean and how do you open this shrine? I've made a roughness 0 glass pane, when I'm in lookdev mode it's reflecting a background that I didn't put there. I know I could just ignore it, but I'd rather be able to see what it'll mostly look like when I'm in the later stages. I also just want to know how on Earth I managed to set this background without realising it  Reflection completely ignores any objects I put in front of it. If I placed this glass inside my house, it would still just reflect trees (This is the point where I felt I couldn't ignore it - reflections are going to play a big part in my project and I don't want to be in render mode all the time)  The nodes are the default glass BSDF, except I set roughness to 0  The glass is set to 20mm thick, if that makes a difference  The background moves with my perspective and moves when I relocate the glass  I have a few HDRI's on my PC, but none look remotely like this   Also, I'm using cycles as I find Evee buggy as hell Objects vs arrays in Javascript for key/value pairs