How to customize the frame background color and borderline width
How does one change the frame size and colors in the frame option of titlesec as in MWE?
How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$? How can one prove the statement $$\lim_{x\to 0}\frac{\sin x}x=1$$ without using the Taylor series of $\sin$, $\cos$ and $\tan$? Best would be a geometrical solution.  This is homework. In my math class, we are about to prove that $\sin$ is continuous. We found out, that proving the above statement is enough for proving the continuity of $\sin$, but I can't find out how. Any help is appreciated. It is quite easy to show that for every prime $p$ and $0&lt;i&lt;p$ we have that $p$ divides the binomial coefficient $\large p\choose i$; one simply notes that in $\large \frac{p!}{i!(p-i)!}$ the numerator is divisible by $p$ whereas the denominator is not (since it is a product of numbers smaller than $p$ and $p$ is prime).  My problem is with generalizing this argument for $q=p^n$. I'm looking for the most elegant and simple way to prove that $p$ still divides $\large q\choose i$. I was reading a bit of Landau and Lifshitz's Mechanics the other day and ran into the following part, where the authors are about to derive the kinetic energy of a free particle. They use the fact that the Lagrangian of this particle must be the same (or at most, differ by the total time derivative of a function of co-ordinates and time) in different inertial frames.     We have $L'=L(v'^2)=L(v^2+2\mathbf{v}\cdot\boldsymbol{\epsilon}+\boldsymbol{\epsilon}^2)$. Expanding this expression in powers of $\boldsymbol{\epsilon}$ and neglecting terms above the first order, we obtain    $$L(v'^2)=L(v^2)+\frac{\partial L(v^2)}{\partial (v^2)}2\mathbf{v}\cdot\boldsymbol{\epsilon}.$$   I think I'm ok with all the physics in this section. What I don't get is just the part I quoted above (so maybe this post is better suited for the math site, but since this is book is so physics-y I thought I'd post it here). My math is pretty rusty, so I'm not really sure- how do the authors expand the function to arrive at the above expression? It reminds me a bit of a Taylor expansion, but not very much. What's the process used to arrive at it? How to disable Windows 10 memory compression? my former wrong assumption: it drains my notebook battery and I've no shortage of RAM. In Task manager you see ntoskrnl.exe is eating more CPU time than any other process. this feature does not appear to be optional and came 2 days ago with the 1st Win10 Update (Win10Pro in my case).  Edit:  I want to disable it, at least to exclude it as a culprit for my (unproven) assumptions. That process never came to my attention in the last 2 months and in task manager's long name it's called "system memory and compressed memory". Let $S = \bigoplus_{n\ge 0} S_n$ be a graded commutative ring. Let $f$ be a homogeneous element of $S$ of degree $&gt; 0$. Let $S_{(f)}$ be the degree $0$ part of the graded ring $S_f$, where $S_f$ is the localization with respect to the multiplicative set $\{1, f, f^2,\dots\}$. Suppose $S$ is finitely generated algebra over $S_0$. Then $S_{(f)}$ is a finitely generated algebra over $S_0$. "It was my op" what does it mean? I heard this in  movie. It was my op. What does it mean? Googling gave me : 'Original Poster'. But that doesn't seem very meaningful. \dots versus \ldots - is there a difference? Is there a difference between \dots and \ldots, the ellipsis?  If yes: Which? When to use \dots and when to use \ldots?  If no: Why are there both at all? Assuming a simple grep such as:  $ psa aux | grep someApp 1000     11634 51.2  0.1  32824  9112 pts/1    SN+  13:24   7:49 someApp   This provides much information, but as the first line of the ps command is missing there is no context for the info. I would prefer that the first line of ps be shown as well:  $ psa aux | someMagic someApp USER       PID %CPU %MEM    VSZ   RSS TTY      STAT START   TIME COMMAND 1000     11634 51.2  0.1  32824  9112 pts/1    SN+  13:24   7:49 someApp   Of course, I could add a regex to grep specifically for ps:  $ ps aux | grep -E "COMMAND|someApp"   However, I would prefer a more general solution as there are other cases in which I would like to have the first line as well.  Seems like this would be a good use case for . Add a legend in an ArcGIS Javascript API I am quite new to Javascript. I have made a html script that includes services I published to ArcGIS for server. It all does exactly what I want and I made it by copying working scripts together and getting help from more experienced scripters. I want to finetune my service by adding a legend. Unfortunately I am not able to create a working script. I have added the parts of my script I assume that are necessary to create my legend. Does anybody see what I am doing wrong?        &lt;script&gt;         var map;         var wmsLayer;         var URL;         var legend;         require(["dojo/query", "esri/map", "esri/layers/WMSLayer", "esri/dijit/Legend", "esri/config", "dojo/domReady!"],         function (query, Map, WMSLayer, Legend, esriConfig) {          esriConfig.defaults.io.proxyUrl = "/proxy/proxy_gcx.php";            map = new Map("map", {               basemap: "topo",               center: [5.5, 52.485],               minZoom: 8,               maxZoom: 13,               zoom: 8,               slider: true           });            wmsLayer = new WMSLayer("URL", {               format: "png",               visibleLayers: ["31", "30", "29", "28"]           });            map.on("layer-add", function (results) {               //add the legend               legend = new Legend({                   map: map,                   layerInfos: [{                       layer: results,                       title: "test"                   }]               }, "legendDiv");               legend.startup();           });             map.addLayer(wmsLayer);       });     &lt;/script&gt; &lt;/head&gt;  &lt;body&gt;     &lt;div id="map"&gt;     &lt;/div&gt;     &lt;div id="legendDiv"&gt;     &lt;/div&gt; &lt;/body&gt;   EDIT: I have edited the code. I am still not done. It does give me a legend on my browser but it says there is no content in there. On my arcgis server manager there is a legend. Balancing long table inside multicol in LaTeX I would like to put some longer tabular data inside the multicols environment while maintaining its balancing abilities. I have tried supertabular with the trick to redefine \newpage as columnbreak. This isn't good though, because the columns aren't properly balanced. Finally I ended up using \halign:  \documentclass[11pt, a4paper]{article} \usepackage[margin=3cm]{geometry} \usepackage{supertabular} \usepackage{multicol}  \def\shortlipsum{\par Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis. Curabitur dictum gravida mauris. Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna. Donec vehicula augue eu neque.\par}  \newcounter{entryno} \setcounter{entryno}{1} \def\tabline{Test &amp; \the\value{entryno} &amp; Description\addtocounter{entryno}{1}\\} \def\tablines{\tabline\tabline\tabline\tabline\tabline} \def\mybreak{\hrule width \columnwidth height 0pt \columnbreak}  \begin{document} \begin{multicols}{2} \shortlipsum \medskip  % % This doesn't balance the columns. Whole table ends up in the left column (it fits) % \begingroup\let\newpage\mybreak % \noindent\begin{supertabular*}{\columnwidth}{@{\indent}l l l} % \tablines\tablines\tablines\tablines\tablines\tablines % \end{supertabular*} % \endgroup  \begingroup\let\\\cr \noindent\halign{\indent#\quad&amp;#\quad&amp;#\hfil\cr \tablines\tablines\tablines\tablines\tablines\tablines} \endgroup  \medskip \shortlipsum \end{multicols} \shortlipsum \end{document}     I was wondering if I'm the only one using \halign to achieve this result. On the other hand supertabular leaves me with an undesired almost empty right column. How would you approach this problem? How do I install Ubuntu 16.04 from an SD card? Could someone explain how to install Ubuntu from an SD card? I don't have any CDs or USB sticks around. My current operating system is Windows 10 64 bit. How to write a function (piecewise) with bracket outside? Per User Named Credential and External Identity Users My question is almost similar to one mentioned in 'Auth Provider with per-user Named Credential' (). I am trying to authenticate and make a API call when a new or existing Salesforce community users try to log in. The Authentication is provided by 3rd party (Cognito). So, the requirement is :  User to be authenticated using the 3rd party system for login. After successful authentication and before community page is displayed, the API call is to be made to 3rd party system to get more details about the user.  In order to achieve this:  Created an Open ID Connect Auth. Provider Use the registration handler on the Auth. Provider to create/link a new/existing user. Use a login flow for API call. Use Per User Identity Type Named Credential to make API calls.  No, where I am having issue is once the user has authenticated successfully, how do I allow the user to make API call without authenticating it again. I am getting the error: An Apex error occurred: System.UnexpectedException: You don't have permission to view this data, enter credentials for the named credential in your personal settings. Or ask your Salesforce admin for help. I believe this error is due to the fact that the user is not listed under 'Authentication setting for External Systems'. My requirement doesn't allow me to authenticate the user again, so how do I achieve this using either APEX or any other way? When I use TikZ tree with nodes with rounded corners, the connecting lines do not touch the nodes (near corners) but end where would rectangle end. Is there an easy way around it?  \documentclass{standalone} \usepackage{tikz} \begin{document} \begin{tikzpicture} [sibling distance=100]    \node[rectangle, draw, rounded corners = 3]{ }   child { node { } }   child { node { } }   ; \end{tikzpicture} \end{document} Is the intersection of a closed set and a compact set always compact? I am going through Rudin's Principles of Mathematical Analysis in preparation for the masters exam, and I am seeking clarification on a corollary.  Theorem 2.34 states that compact sets in metric spaces are closed. Theorem 2.35 states that closed subsets of compact spaces are compact. As a corollary, Rudin then states that if $L$ is closed and $K$ is compact, then their intersection $L \cap K$ is compact, citing 2.34 and 2.24(b) (intersections of closed sets are closed) to argue that $L \cap K$ is closed, and then using 2.35 to show that $L \cap K$ is compact as a closed subset of a compact set.  Am I correct in believing that this corollary holds for metric spaces, and not in general topological spaces? Let $\sim$ denote the equivalence relation on the $n$-sphere $S^n$ defined via   $$ (x_1,\dots,x_n,x_{n+1})\sim(x_1,\dots,x_n,−x_{n+1})\:\text{ for all }\: (x_1,\dots,x_{n+1})\in S^n. $$      Show that the quotient space $S^n/\sim$ is homeomorphic to the $n$-disc $D^n$.   I know that Ii have to show that there exists a bijective function $f: (S^n/\sim) \to D^n$ that is continuous and that the pre-image $f^{-1}$ is continuous as well, but I can't advance from here, any tips? Unable to correctly install pip3 using apt-get I am using Ubuntu 16.04, and was experiencing issues with my pip3. Specifically, when I attempted to uninstall a package via  sudo pip3 uninstall   I encountered   Traceback (most recent call last):   File "/usr/bin/pip3", line 9, in &lt;module&gt;     from pip import main ImportError: cannot import name 'main'   I attempted to resolve this issue by reinstalling pip3, specifically   sudo python3 -m pip uninstall pip &amp;&amp; sudo apt install python3-pip --reinstall   which succeeded. However, I no longer have a local version of pip3 at all  bash: /home/kurt/.local/bin/pip3: No such file or directory   Using which pip3 in a new terminal I find,  $ which pip3 /usr/bin/pip3   and attempting to use pip3 at all brings me  $ pip3 Traceback (most recent call last): File "/usr/lib/python3/dist-packages/pip/_vendor/__init__.py", line 33, in vendored     __import__(vendored_name, globals(), locals(), level=0) ImportError: No module named 'pip._vendor.pkg_resources'  During handling of the above exception, another exception occurred:  Traceback (most recent call last): File "/usr/bin/pip3", line 9, in &lt;module&gt;     from pip import main File "/usr/lib/python3/dist-packages/pip/__init__.py", line 13, in &lt;module&gt;     from pip.exceptions import InstallationError, CommandError, PipError File "/usr/lib/python3/dist-packages/pip/exceptions.py", line 6, in &lt;module&gt;     from pip._vendor.six import iteritems File "/usr/lib/python3/dist-packages/pip/_vendor/__init__.py", line 75, in &lt;module&gt;     vendored("pkg_resources") File "/usr/lib/python3/dist-packages/pip/_vendor/__init__.py", line 36, in vendored     __import__(modulename, globals(), locals(), level=0) File "&lt;frozen importlib._bootstrap&gt;", line 969, in _find_and_load File "&lt;frozen importlib._bootstrap&gt;", line 958, in _find_and_load_unlocked File "&lt;frozen importlib._bootstrap&gt;", line 664, in _load_unlocked File "&lt;frozen importlib._bootstrap&gt;", line 634, in _load_backward_compatible File "/usr/share/python-wheels/pkg_resources-0.0.0-py2.py3-none-any.whl/pkg_resources/__init__.py", line 2927, in &lt;module&gt; File "/usr/share/python-wheels/pkg_resources-0.0.0-py2.py3-none-any.whl/pkg_resources/__init__.py", line 2913, in _call_aside File "/usr/share/python-wheels/pkg_resources-0.0.0-py2.py3-none-any.whl/pkg_resources/__init__.py", line 2952, in _initialize_master_working_set File "/usr/share/python-wheels/pkg_resources-0.0.0-py2.py3-none-any.whl/pkg_resources/__init__.py", line 956, in subscribe File "/usr/share/python-wheels/pkg_resources-0.0.0-py2.py3-none-any.whl/pkg_resources/__init__.py", line 2952, in &lt;lambda&gt; File "/usr/share/python-wheels/pkg_resources-0.0.0-py2.py3-none-any.whl/pkg_resources/__init__.py", line 2515, in activate File "/usr/share/python-wheels/pkg_resources-0.0.0-py2.py3-none-any.whl/pkg_resources/__init__.py", line 2097, in declare_namespace File "/usr/share/python-wheels/pkg_resources-0.0.0-py2.py3-none-any.whl/pkg_resources/__init__.py", line 2047, in _handle_ns File "/usr/share/python-wheels/pkg_resources-0.0.0-py2.py3-none-any.whl/pkg_resources/__init__.py", line 2066, in _rebuild_mod_path AttributeError: '_NamespacePath' object has no attribute 'sort'   However, I am able to execute without incident when typing sudo -H pip3 -v. Reinstalling pip3 from apt, e.g.  sudo apt-get install python3-pip --reinstall   has no effect. If anyone has any insight, or has encountered a similar problem, I would greatly appreciate any input on how to approach this problem. How are Anonymous inner classes used in Java? What is the use of anonymous classes in Java? Can we say that usage of anonymous class is one of the advantages of Java? Something small goes wrong, and this triggers something slightly bigger, which triggers something slightly bigger, and so on and so forth until you end up with a chain of problems of increasing severity until it ends in catastrophy.  Something like the old saying "for want of a nail the battle was lost", only highlighting that each intermediate issue was a problem in its own right, not just a stepping-stone to the final disaster.  Is there a common word/phrase that specifically describes this? I'm thinking "cascade of ever-increasing problems", but this seems clumsy, and I suspect there might already be a neat word or expression that covers it. What is the difference between old style and new style classes in Python?