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Fundamental Theorem of Calculus. Fundamental Theorem of Calculus says  Let $f$ be an integrable function on $[a,b].$ For $x$ in $[a,b],$  let $F(x)=\int_{a}^{x}f(t)dt.$ Then $F$ is continuous on $[a,b].$ If $f$ is continuous at $x_{0}$ in $(a,b),$ then $F$ is differentiable at $x_{0}$ and $F^{'}(x_{0})=f(x_{0}).$  Now my question is why we are saying that this is "Fundamental Theorem of whole Calculus".  It is clear that it connects intergal and differential calculus. But i am not getting the exact concept, why this is so important as its name is fundamental theorem of calculus. Why we says that it is fundamental theorem of calculus?  Please suggest me. Thanks in advance. AJAX select returns 'illegal choice detected' Create a settings form for a module in Drupal 8 - when a user selects a View from a list, the drop down under it should populate with the displays in that view.  While the form updates the option list for the user, it also throws an error message on the screen "Illegal choice has been detected".  Here is the code (it doesn't paste very well):    getViewDisplays is the ajax callback that is populating the options.  Some people who have posted about this around the internet say to set #validated on the select field to TRUE, though, that doesn't necessarily feel right. I still want to validate the submission to do some checks. How do I display a decimal value to 2 decimal places? When displaying the value of a decimal currently with .ToString(), it's accurate to like 15 decimal places, and since I'm using it to represent dollars and cents, I only want the output to be 2 decimal places.   Do I use a variation of .ToString() for this? Mass dropped on a spring I thought this would be a particularly simple problem but it is turning out to be quite the opposite. I am sure I am doing a very simple mistake.   The problem statement is that there is a mass which is just barely kept on the spring (help by the force equal to the weight of the spring) such that the spring is uncompressed. As soon as I let the object go, it will compress the spring and come to rest at some height. The energy stored in the spring will be equal to the difference in the potential energy at the two height of the spring (compressed and uncompressed),  $$mgh_i -mgh_f= 1/2 kx^2$$ Furthermore, the compression of the spring would just be the difference in the $h_f -h_i$. This gives me two roots for compression,  $$ x=0 $$ And the second would be, $$ mg=1/2kx $$ But then by this, $kx=2mg$ and $kx$ is force by Hooks law, but then does it means that the force compressing the spring is twice the weight of the object? That sounds odd. I was expecting I would just recover Hooks law but I guess I am doing something wrong here. But I am not sure what that is.   Any help will be much appreciated.  P.S. This is not a homework problem. We are designing a project for our school.  Thanks for your time. Looks like flagging has been affected by releases today. Are these intended effects?   Higher daily limits (appear doubled for me, flagging of posts limit also doubled).  Explained by Shog9 below. Soft comment deletion  - e.g. for "accept rate" obsolete comments - it does in fact work, but the immediate feedback is gone.  This is fixed now. Has the throttling rate changed?  Seems possible to repeated flag without waiting 5 seconds.  If it was broken, it isn't anymore. Old soft deletions that were neither categorised as "helpful" or "declined" have all become "helpful".   If limits have been updated, can we get the new formula published? Not changed, as confirmed by Shog9. Page number in title page I want to add page number from 531 to 536 in my latex IEEE conference template. But page number appearing from page 2 i.e. 532.  \documentclass[conference]{IEEEtran} %\IEEEoverridecommandlockouts  \makeatletter \let\old@ps@headings\ps@headings \let\old@ps@IEEEtitlepagestyle\ps@IEEEtitlepagestyle \def\confheader#1{%     % for all pages except the first     \def\ps@headings{%         \old@ps@headings%         \def\@oddhead{\strut\hfill#1\hfill\strut}%         \def\@evenhead{\strut\hfill#1\hfill\strut}%     }%     % for the first page     \def\ps@IEEEtitlepagestyle{%         \old@ps@IEEEtitlepagestyle%         \def\@oddhead{\strut\hfill#1\hfill\strut}%         \def\@evenhead{\strut\hfill#1\hfill\strut}%     }%     \ps@headings% } \makeatother  \confheader{ 2020 IEEE International Conference on Computation, Automation and Knowledge Management (ICCAKM) }   %%footer %\usepackage[pscoord]{eso-pic} %\newcommand{\placetextbox}[3]{ %   \setbox0=\hbox{#3} %   \AddToShipoutPictureFG*{ \put(\LenToUnit{#1\paperwidth},\LenToUnit{#2\paperheight}){\vtop{{\null}\makebox[0pt][c]{#3}}} %   } %} %\placetextbox{.23}{0.055}{\small{978-1-5386-8007-0/19/\$31.00~\copyright 2019 IEEE}}     \usepackage{cite} \usepackage{amsmath,amssymb,amsfonts} \usepackage{algorithmic} \usepackage{graphicx} \usepackage{textcomp} \usepackage{xcolor} \usepackage{float} \usepackage[export]{adjustbox} \usepackage{subcaption}     % %\usepackage[pscoord]{eso-pic} %\newcommand{\placetextbox}[3]{ %   \setbox0=\hbox{#3} %   \AddToShipoutPictureFG{ \put(\LenToUnit{#1\paperwidth},\LenToUnit{#2\paperheight}){\vtop{{\null}\makebox[0pt][c]{#3}}} %   } %} %\placetextbox{.2}{0.055}{978-1-4799-5522-0/15/\$31.00~\copyright 2015 IEEE}   \IEEEoverridecommandlockouts \IEEEpubid{\makebox[\columnwidth]{978-1-7281-0666-3/20/\$31.00~\copyright~2020         IEEE \hfill} \hspace{\columnsep}\makebox[\columnwidth]{ }}      \thispagestyle{plain}     \pagestyle{plain}     \setcounter{page}{531}   \begin{document}  \title{Performance Analysis of Physically     Unclonable Function Based on Voltage Divider Arrays} \author{\IEEEauthorblockN{Sumit Chaudhary$^{1}$}     \IEEEauthorblockA{\textit{Dept. of Electronics and Communication} \\         \textit{MNIT Jaipur, India}\\         2016pev5165@mnit.ac.in}     \and     \IEEEauthorblockN{Chitrakant Sahu$^{2}$}     \IEEEauthorblockA{\textit{Dept. of Electronics and Communication} \\         \textit{MNIT Jaipur, India}\\         chitrakant.ece@mnit.ac.in}}  \maketitle   \end{document} DML Statement in ‘after trigger’ and not in ‘before trigger’? I was shooting the lighting of the city that is visible at the top of the trees if you shoot landscape.  No matter what I do, the image is blurry. What have i done:   ISO 100 Manual focus towards infinity Using a tripod Using really sharp prime &amp; good camera   Basically, everything I could. The only example i have is here, but it is not good, because image is underexposed:    The main question: Why can't night photographs be as sharp as daily photographs (with approperiate exposure times of course)? Creating a new DOM element from an HTML string using built-in DOM methods or Prototype I have an HTML string representing an element: '&lt;li&gt;text&lt;/li&gt;'. I'd like to append it to an element in the DOM (a ul in my case). How can I do this with Prototype or with DOM methods?  (I know i could do this easily in jQuery, but unfortunately we're not using jQuery.) Green is the most common circuit-board color because it has become an industry standard.  What I'm interested in is How the traditional "PCB Green" become a standard in the first place?   Were there any interesting historical reasons for the initial choice, or was it just a product of what one particularly successful company was doing that became the de-facto standard? I've been to South Korea a few times already and always enjoy it but I've always had an onward ticket before.  Now I need to fly home from a trip that's lasted over a year, but I still want to take my time and keep my options open.  There's a good choice of cheap flights from Istanbul to Seoul and from Seoul I can't decide yet whether to fly straight home or take a ferry to China, hitchhike to Guangzhou, and get a cheap flight home from there.  I can't really just buy the China-Australia flight now because I'm not sure yet whether I'll be able to get the Chinese visa easily enough or how long my remaining money will last.  I know Korea, like most countries, has rules saying you need an onward ticket, but in my experience many countries never try to verify that you have this ticket unless you fit some profile. So in this instance I would find first-hand knowlegde much more informative that pointers to a government website.  In practice does South Korea admit tourists with one-way tickets? Sometimes you see a video of a fan or a propeller spinning very fast, and the apparent rotation is distorted. The fan can appear to be moving in the opposite direction of rotation, or even stationary. This optical illusion is known as the wagon-wheel effect. If I understand correctly, this occurs because the camera framerate is slower than the frequency at which the fan makes one rev, so stroboscopic effects should be expected.   Does the wagon-wheel effect occur only in videos, or can we observe it just with the eye? Let $\displaystyle f$ be differentiable, $\displaystyle f(x)=0$ for $|x| \geq 10 $ and $g(x)=\sum_{k \in \mathbb Z}f(x+k).$ I've encountered different usages of preposition + Home and I want to learn which of them are correct.  Some examples:     Back home   Back at home   Back to home Can I travel in UK before switching to a study visa? As I read in general visitor visa Terms &amp; Condition, I would only be granted to stay up to 6 months in UK. However I am planning to apply for General Student Visa to further my studies. Would it be possible for me to enter UK as visitor for first 6 months/less before I apply for student visa in the same year if I want to travel and study on the same year? How can I highlight text before a character with listing? All is in the title. I would like to add a color to the text before a character with listing package.  For example, I would like to add a color to text between the beginning of a line and : or =, in a makefile.  I tried to use moredelimiters but I did not succeed.    \documentclass{article}  \usepackage{listings} \usepackage{xcolor} \definecolor{keycolor}{RGB}{172, 42, 42} \definecolor{mbleu}{RGB}{64,96,127} \definecolor{vimvert}{RGB}{46, 139, 87}  \lstdefinestyle{global}{   basicstyle=\ttfamily\scriptsize\color{black!90},%   stringstyle=\itshape\color{magenta},%   showstringspaces=false,%   keywordstyle={\bfseries\color{keycolor}},%   commentstyle=\color{blue}\slshape,%   framexleftmargin=1mm,%   backgroundcolor=\color{black!2},% }  \lstdefinestyle{makefile}{   style=global,%   morecomment=[l][commentstyle]{\#},%   emphstyle={\color{vimvert}},%   moredelim=[s][emphstyle]{\$(}{)}% }  \begin{document}  \begin{lstlisting}[style=makefile] .SUFFIXES: .inc .f .f90 .F  # all CPP processed fortran files have the extension .f90 SUFFIX=.f90  #----------------------------------------------------------------------- # this release should be fpp clean # we now recommend fpp as preprocessor # if this fails go back to cpp CPP_=fpp -f_com=no -free -w0 $*.F $*$(SUFFIX)  vasp: $(SOURCE) $(FFT3D) $(INC) main.o      rm -f vasp     $(FCL) -o vasp main.o  $(SOURCE)   $(FFT3D) $(LIB) $(LINK) makeparam: $(SOURCE) $(FFT3D) makeparam.o main.F $(INC)     $(FCL) -o makeparam  $(LINK) makeparam.o $(SOURCE) $(FFT3D) $(LIB) zgemmtest: zgemmtest.o base.o random.o $(INC)     $(FCL) -o zgemmtest $(LINK) zgemmtest.o random.o base.o $(LIB) dgemmtest: dgemmtest.o base.o random.o $(INC)     $(FCL) -o dgemmtest $(LINK) dgemmtest.o random.o base.o $(LIB)  ffttest: base.o smart_allocate.o mpi.o mgrid.o random.o ffttest.o $(FFT3D) $(INC)     $(FCL) -o ffttest $(LINK) ffttest.o mpi.o mgrid.o random.o smart_allocate.o base.o $(FFT3D) $(LIB) kpoints: $(SOURCE) $(FFT3D) makekpoints.o main.F $(INC)     $(FCL) -o kpoints $(LINK) makekpoints.o $(SOURCE) $(FFT3D) $(LIB)  clean:       -rm -f *.g *.f *.o *.L *.mod ; touch *.F \end{lstlisting}  \end{document} So I have a generic list, and an oldIndex and a newIndex value.  I want to move the item at oldIndex, to newIndex...as simply as possible.  Any suggestions?  Note  The item should be end up between the items at (newIndex - 1) and newIndex before it was removed. I'm running an SSH server on my personal computer. The log had many people(or bots?) repeatedly trying to log in to my server (that is before I changed the default port), which made me a little freaked out. I was worried about their dictionary attacks or brute force password guessing.  But then if you type wrong password (or wrong username), the server waits for about 2 seconds before it asks for password again. So an attacker can try one password per 2 seconds. So I concluded that these attacks aren't that great a threat (as long as your password does not consist of dictionary words.) Am I correct? Why does Ubuntu create a file ending in ~ for every file I create with a text editor like GNU Emacs? Restoring backups failing Ubuntu 16.04