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Inequality of $\vert \text{tanh}(x)-x+\frac{x^3}{3}\vert\leq\frac{1}{8}$ for $x\in[-1/4,1/4]$ I have an assignment, that I cannot seem to find a starting point for. I am not looking for the specific answer, but only where to begin. Any pointers are appreciated.  I have to prove the inequality $\vert \tanh(x)-x+\frac{x^3}{3}\vert\leq\frac{1}{8}$ for $x\in[-1/4,1/4]$ where $x-\frac{x^3}{3}$ is the 3rd order Taylor expansion.  I've tried with the triangle inequalities, Lagrange remainders, and a lot of other stuff, but I am no where near a correct argumentation. Does anyone have any suggestions? latex table border dont appear / to big / to small How do you make a test class for custom controller? My search results involves this but trying to apply it in my test class only create too many error that I don't understand.  public static testMethod void testMyController() {     PageReference pageRef = Page.success;//Observe how we set the Page here     Test.setCurrentPage(pageRef);   . Does my test class need those line of codes when my controller class is only very simple.  public class ClientInfo_VFcontroller{     public Org_Info__c orgInfo {get; set;}     public ClientInfo_VFcontroller(){         orgInfo = new Org_Info__c();     }     public PageReference save(){         insert orgInfo;         orgInfo = null;         ScheduleRetrieve.ScheduleRetrieve();         return null;     } } Number of non decreasing sequences of length $M$ How many non decreasing sequences are there of length $M$, provided the number in the sequences are allowed from $1,2,3,...,N$? Stuck at 0% [waiting for headers] On googling this error it seems that a lot of people are having this issue.  apt-get upgrade hangs at 0% [waiting for headers] apt-get install apache2 hangs at 0% [waiting for headers]. Some apt-get commands are working, but only certain packages.  Any ideas? I don't think this is an issue with slow repos because I've had it up for a long while and it hasn't budged from 0%. I have edited sources.list but I removed the lines I added when this issue presented itself and it hasn't made a difference.  Any clues would be really useful. Sum of reciprocals of numbers with certain terms omitted In C the following horror is valid:  myFunc() {   return 42;  // return type defaults to int. }   But, what about in C++? I can't find a reference to it either way...  My compiler (Codegear C++Builder 2007) currently accepts it without warning, but I've had comments that this is an error in C++. How to allocate aligned memory only using the standard library? I just finished a test as part of a job interview, and one question stumped me, even using Google for reference. I'd like to see what the StackOverflow crew can do with it:  The memset_16aligned function requires a 16-byte aligned pointer passed to it, or it will crash. a) How would you allocate 1024 bytes of memory, and align it to a 16 byte boundary? b) Free the memory after the memset_16aligned has executed.  {        void *mem;    void *ptr;     // answer a) here     memset_16aligned(ptr, 0, 1024);     // answer b) here     } I recently made the switch to Ubuntu. Everything on my laptop works fine except my hybrid graphics card. It is Intel graphics combined with Nvidia GeForce GT650M. I tried Bumblebee, but primusrun doesn't work (segmentation fault, core dumped) and optirun works with glxspheres64, but steam games look worse with optirun than with Intel graphics (e.g. Surgeon Simulator 2013 runs fine with Intel and hangs a lot with optirun)   I tried Nvidia Prime, but it gives me a black screen on startup after install, so I can't do anything and have to power off my PC with the power button. I also tried nvidia-prime 0.5 on Ubuntu 14.04, and then I get 'low-graphics mode' and I can't get to Unity. Recently I've changed jobs, and consequently the field of research has also changed. But I'm still getting proposals for publications in the previous field, and it is interesting for me to accept some of them. My concern is about which affiliation to use: on one hand I gain all the knowledge in that field while working on the previous employer, also I hope they can cover my expenses related to the publication. On the other hand, I do not work for them anymore, and my current company has very little interest in my old field of research, and probably will not support it financially, but I think it is wise to mention them as well. As a compromise I'm thinking to put the previous employer in the affiliation, and the name of my new employer in the footnote, something like "currently at XYZ". Surely I'll discuss this issue with both, although the opinion of the community is also very valuable. What is the difference between "retired out" and "retired not out" in cricket? How can I solve the folowing Diophantine equation with two unknowns? Find one integer solution to the following Diophantine equation:   \begin{equation*} \\\forall \,x,y \in \mathbb{Z}\\ 6xy + x - y = 274 \end{equation*}   The resultat ist $x = 9$, $y = 5$ (Obtained with  )  I need to know a method that allows me to reach such a result. How can I calculate the value of these two variables in a Diophantine equation? For example: 6xy + x - y = 458 Can you cast a 9th level spell if your multiclass spell slots have 9th level spell slots? Is there a nice solution to get a "presenter mode" for Latex presentations? I really like the way Keynote and MS Office (and also OpenOffice &amp; similar) support a presentation mode that displays the current slide, the next (and maybe previous) slide, the elapsed and current time, and also any notes attached to the slides on one screen and the presentation itself on the beamer/second screen.  It enables me to give good, professional presentations without having to know everything by heart (I suck at that).  I found a , but I am looking for alternatives, especially OS-independent would be great. Not having to create 3 different PDFs is a boon.  Any hints? Does it look good to edit the question you're answering? I have a question about editing practices:  Does it look good to edit a question you have just answered?  For example: say I had just answered a question, then saw that the question had some minor formatting issues. Should I edit it? Does it turn up voters off when they see that I am answering a question I changed, possibly to better suit my answer? New Graphics Card Preventing Boot Up Comparison between bootstrap percentiles confidence interval and BCa confidence interval? I have generated a nonparametric percentiles bootstrap confidence interval ($32.27143, 51.08571$), and a BCA confidence interval ($33.26, 53.49$) with an initial sample size of $n=7$.  Evidently, the BCA interval is larger than the percentiles interval. Shouldn't the BCA interval be better than the percentiles interval (and by "better" I mean "smaller")? I noticed also that when the sample size is larger, for example $n=40$, BCa confidence interval decreases. so I stumbled upon this equation/formula, and I have no idea how to prove it. I don't know how should I approach it: $$ \sqrt{2 + \sqrt{2 + \cdots + \sqrt{2 + \sqrt{\vphantom{\large A}2\,}\,}\,}\,}\ =\ 2\cos\left(\vphantom{\Large A}\pi \over 2^{n + 1}\right) $$  where $n\in\mathbb N$ and the square root sign appears $n$-times.  I thought about using sequences and limits, to express the LHS as a recurrence relation but I didn't get anywhere.  edit: Solved, thanks for your answers and comments. Search functionality in lightning:datatable? Is there a way to search across all rows/columns in a lightning:datatable to narrow down the list, just like jQuery DataTables? If so, how do implement that?  Can I somehow do it all on the client-side to make it super fast (some sort of DOM manipulation)  I'm having some issues with the lightning:datatable not updating. I have attached my code below, maybe you can help me spot the issue:  Markup:  &lt;aura:component extends="c:Base" controller="AccountBrowserForm"&gt; &lt;aura:handler name="init" value="{! this }" action="{! c.doInit }"/&gt; &lt;aura:attribute name="selectedAccountId" type="Id" access="public" /&gt; &lt;aura:attribute name="accounts" type="Object"/&gt; &lt;aura:attribute name="mycolumns" type="List"/&gt; &lt;aura:attribute name="sortedBy" type="String" /&gt; &lt;aura:attribute name="sortedDirection" type="Boolean" default="true" /&gt;  &lt;aura:registerEvent name="AccountFilterChange" type="c:AccountFilterChange" /&gt;  &lt;aura:attribute name="backingdata" type="List" /&gt; &lt;aura:attribute name="filter" type="String" /&gt; &lt;lightning:input type="text" onchange="{!c.filter}" value="{!v.filter}" label="Filter" /&gt;  &lt;lightning:datatable aura:id="lightningTable"                      data="{! v.accounts }"                      columns="{! v.mycolumns }"                      keyField="Id"                      onrowaction="{! c.handleRowAction }"                      onsort="{!c.updateColumnSorting}"                      sortedBy="{!v.sortedBy}"                      sortedDirection="{!v.sortedDirection}"                      hideCheckboxColumn="true" /&gt;     Controller:  doInit: function (component, event, helper) {     helper.callServer(component, "c.getAccounts", $A.getCallback(function (response) {         component.set("v.accounts", response);         component.set("v.backingdata", response);         console.log(component.get("v.backingdata") + " /// BACKING DATA INSIDE ")         console.log(component.get("v.accounts") + " // ACCOUTN DATA INSIDE")          component.set('v.mycolumns', [{                 type: "button",                 typeAttributes: {                     label: '',                     iconName: 'utility:add',                     name: 'selectRecord',                     title: 'selectRecord',                     disabled: false,                     value: 'edit',                     variant: {                         fieldName: 'variantValue'                     },                 }             },             {label: 'Name', fieldName: 'Name', type: 'text', sortable: true},             {label: 'Street', fieldName: 'BillingStreet', type: 'text', sortable: true},             {label: 'Postal Code', fieldName: 'BillingPostalCode', type: 'text', sortable: true},             {label: 'City', fieldName: 'BillingCity', type: 'text', sortable: true},             {label: 'Country', fieldName: 'BillingCountry', type: 'text', sortable: true},         ]);          console.log(component.get("v.backingdata") + " *** BACKING DATA OUTSIDE *** ")         console.log(component.get("v.accounts") + " *** ACCOUNT DATA OUTSIDE *** ")     })) },  filter: function (component, event, helper) {     var data = component.get("v.backingdata"),         term = component.get("v.filter"),         results = data,         regex;     try {         regex = new RegExp(term, "i");         // filter checks each row, constructs new array where function returns true         results = data.filter(row =&gt; regex.test(row.name) || regex.test(row.age.toString()));     } catch (e) {         // invalid regex, use full list     }     component.set("v.accounts", results); },   For some reason the filter function is completely unresponsive. Also, does it matter that I'm populating the component with a response from a callback function. @sfdcfox, I noticed in your example that you simple created an array with dummy data. My "myaccounts" attribute is of type object I am aware of the basics of evolutionary theory, however I don't understand how mutations can add genes over time.   Am I correct in thinking that creatures within the same species who mutate to have an additional gene in their genome would normally be infertile?  Or am I misunderstanding that?  Can someone explain the process of the creation of genetic material through evolution?  Citation to a decent academic paper or book on the matter would be appreciated too.