I want to prove that $\sin(x)$ is continous in $\mathbb R$, the definition that I have of $\sin(x)$ is the definition of the Spivak's book (the geometric one), but maybe using some other definition would make   the prove easier?
How do I prove $\sin x$ is uniformly continuous on $\mathbb R$ with delta and epsilon?   I proved geometrically that $\sin x&lt;x$ and thus, $$|f(x_1)-f(x_2)|=|\sin x_1 - \sin x_2|\le|\sin x_1|+|\sin x_2|&lt;|x_1|+|x_2|$$   But this doesn't help me much finding a delta...   Thanks for any help!  P.S. I'm only at the beginning of calculus so I can't use many theorems and derivation  (because they haven't been regorously proven).
Status of B1/B2 visa after citizenship change? I have a valid B1/B2 visa valid to US till March 2019 on Indian passport, I changed my citizenship to Australian. Is my B1/B2 visa on Indian passport valid? How to remove title entry in the bibliography contents? I use plain bibliography style for my book. When I compile it, by default, I get the details including the title in my reference. like this:     H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, a. Dinola, and J. R. Haak. Molecular dynamics with coupling to an external bath. J. Chem. Phys., 81:3685-3690,1984.   This is too long and I have more than 100 such references which makes the document too long. How can I force it to remove the title from this reference? something like this:     H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, a. Dinola, and J. R. Haak.  J. Chem. Phys., 81:3685-3690,1984.   Your answer will be greatly appreciated.  By the way, I still would like to use the plain bibliography style. What is the state-of-the-art method for automatically executing custom scripts upon USB device plug-in under current Linux distributions like Debian/CentOS/Fedora?  For example if you want to automatically mount/copy some files/umount a USB mass storage device based on its UUID (or device ID etc.). What is the penalty for dual US citizens who lie on the ESTA form in order to enter under VWP using their second passport? How do I check if an element is hidden in jQuery? Is it possible to toggle the visibility of an element, using the functions .hide(), .show() or .toggle()?  How would you test if an element is visible or hidden? Pretty much the problem asks if a function is continuous at the point $c$ and $f(c) &gt; 0$ then there exists a $d &gt; 0$ such that $\forall x$, $f(x) &gt; 0$ with $|x-c| &lt; d$.   I can understand what the problem means. That if a function is positive at a point then there is another point that's really close that'll also be positive. I can not prove this in a formal way though. I've tried using the intermediate value theorem and I do not know hot to implement it. Any ideas? ST_Length (GEOM, true) for calculating distances in Geographic Reference System Bold code in a question Frequently when I ask a question I have to include quite a bit of code for reference purposes.    It would be nice to be able to bold the important lines in the code.  For example this code:  &lt;DataTrigger Value="True"&gt;     &lt;DataTrigger.Binding&gt;         &lt;MultiBinding Converter="{StaticResource DisableWorkItemConverter}"&gt;             &lt;Binding ElementName="MainForm" Path="PickedWorkItemID"/&gt;             &lt;Binding Path="Id"/&gt;         &lt;/MultiBinding&gt;     &lt;/DataTrigger.Binding&gt;     &lt;Setter Property="IsEnabled" Value="False"/&gt;     &lt;Setter Property="IsSelected" Value="False"/&gt; &lt;/DataTrigger&gt;   Is not way long, but the important part (as seen in ) is the second to last line.  However, if I try to bold it, it ends up looking like this:  &lt;DataTrigger Value="True"&gt;     &lt;DataTrigger.Binding&gt;         &lt;MultiBinding Converter="{StaticResource DisableWorkItemConverter}"&gt;             &lt;Binding ElementName="MainForm" Path="PickedWorkItemID"/&gt;             &lt;Binding Path="Id"/&gt;         &lt;/MultiBinding&gt;     &lt;/DataTrigger.Binding&gt;     &lt;Setter Property="IsEnabled" Value="False"/&gt;     **&lt;Setter Property="IsSelected" Value="False"/&gt;** &lt;/DataTrigger&gt;   Not what I was going for.  It would be nice to be able to draw attention to specific lines of code when needed.    (One suggestion of a different color background sounds nice too (ie a yellow background to draw the eye to the relevant code.)  If there is some other way to bold in code please let me know. How can I stop certain apps from appearing in the Dash? The following MWE produces a PDF whose TOC has two entries: “Foo” and “Bar” with correct page numbers. So far, so good. However, upon clicking on the link to “Bar”, I am taken to the page for “Foo” instead.  \documentclass{report} \usepackage{hyperref} \newcommand*\backmatter{\setcounter{chapter}{0}}  \begin{document} \tableofcontents \chapter{Foo} \backmatter \chapter{Bar} \end{document}   (Produced with pdflatex, run twice.)  This MWE is whittled down from a (much!) more complex document but the above does seem to reproduce the error reliably.  Re-setting the chapter count seems to confuse hyperref, even though the page references are still accurate. Notice that in my real document, \backmatter does other things, including setting the numbering style to alphabetical so there’s no chance of confusion even though both chapters are ostensibly labelled as “Chapter 1”.  How do I fix this? Is this a bug? Are there workarounds? A bounce-rate attack to manipulate SEO? This is a question to experienced people that might help us shed some light on the issue.   We noticed a very strange behavior on our site, in Google Analytics. Some dude from Finland, namely, from Kouvola city is hitting one of our pages - only one page on our site, 'bout a hundred times per day, all with an average bounce rate of 90%+...  This is causing our overall bounce rate to go up by 1 to 3% per day... which is very disturbing.. since we're trying to do our best in order to keep it as low as possible. And obviously having it jumped from ~24% to 27%, just because of that crazy dude is not making us happy at all... We tried implementing a geo-targeted script in order to catch this particular visitor and deliver him a juicy message, and it seemed like it helped in the beginning, it has stopped for a day or two, but now he's back...   The geo-targeted script was also logging all IP addresses for page requests originating from Finland in order to find out more details and (in order to block them on the server level, later).. but thing is, it was all mainly cable or DSL connections with various, but not constantly repeating IPs... we are all wondering what is he up to really ?   I think that this page should be kept updated with ideas on how to combat this and perhaps someone could also shed light on what it might be ? What is the reason for doing this "bounce-rate attack", as I call it?  There was a similar question asked on stackoverflow earlier, with no meaningful answer - here - Minecraft webpage links in chat? What triggers a full garbage collection in Java? Delete all data in Postgres database leaving oil on a frying pan for use later I live alone, so I cook for myself. And often times I cook steaks/burgers on a pan, and later in the same day would return to use the same pan/oil without washing/using new oil.  Is this safe, or should one wash and use a new pan before cooking every steak/burger patties? I've actually done this for more than a day once (cooked burgers in the morning, steaks later that afternoon, and then burgers for the next morning). I met this equation frequently in Guass-Newton optimizations. But I dont understand why the left and right side of the equation can be equal.  Lets say the Jacobian is $2$ by $2$   and Hessian is $$\begin{bmatrix}\frac{\partial^2f_1}{\partial^2 x_1 } &amp; \frac{\partial^2f_1}{\partial^2 x_2  } \\ \frac{\partial^2f_2}{\partial^2 x_1 } &amp; \frac{\partial^2f_2}{\partial^2 x_2  }\end{bmatrix}$$   But the right hand side of the equation is  $$J^TJ =\begin{bmatrix} \left( \frac{\partial f_1}{\partial x_1} \right)^2 + \left( \frac{\partial f_2}{\partial x_1} \right)^2  &amp;  \frac{\partial f_1}{\partial x_1}\frac{\partial f_1}{\partial x_2} +\frac{\partial f_2}{\partial x_1}\frac{\partial f_2}{\partial x_1}\\ \frac{\partial f_1}{\partial x_1}\frac{\partial f_1}{\partial x_2} +\frac{\partial f_2}{\partial x_1}\frac{\partial f_2}{\partial x_1} &amp;\left( \frac{\partial f_1}{\partial x_2} \right)^2 + \left( \frac{\partial f_2}{\partial x_2} \right)^2\end{bmatrix} $$  Why can these two be equal as presented in papers? LWC Get Pick-list Field Values In LWC, is it possible to get a pick-list field's possible values?  I'm writing a component that is embded into a lightning record page. I need my component to be able to load the record from the page, get data from the fields and use that data to pre-populate my search form with default values.  I have this working with city/state and checkbox fields. Right now the city/state fields are built pull data from an aggregate query of contacts to find all possible state/city combinations (I know this is doomed to fail when the records reach over 50k contacts but Its good enough for now).  I have a pick-list field on my object called skill level, I need to be able to build a combo box that has all the possible values for skill level and set the default value to the value on the associated record.  I'd like to avoid hard-coding the available options if possible.  In LWC, is it possible to get a pick-list field's possible values? What is the Ubuntu equivalent of this interface?    I am looking for a user-friendly method that the owner of a computer can use to log off other users without having to restart.  The case I'm concerned about is of the beginner-level user who needs administrative control over the computer because they are the owner, but probably isn't concerned with most of the tasks we would usually associate with system administration. What is a token? Please forgive such a basic question, but I did some Google searching and looked around on this site,  and while there are many threads and online resources that involve tokens, I can't seem to find a direct explanation of what a token is, specifically in the context of TeX, LaTeX, etc. Perhaps there is a good explanation of tokens in the TeXbook, but I don't have a copy of it.   gives me some idea:     A token is a string of characters, categorized according to the rules as a symbol (e.g., IDENTIFIER, NUMBER, COMMA).   but this is a bit too general for me to understand. Taking a guess based on the Wikipedia definition and , is it correct to say that a token is "a thing that has a catcode"? (which, even if true, does not seem entirely satisfactory as an answer: what characterizes the things that are given catcodes?)  Some illustrative examples, and non-examples, of tokens in the realm of TeX, LaTeX, etc. would be much appreciated. How to use aes-encryption in PostgreSQL? I tried aes-encryption by using following statement:  SELECT encrypt('test', 'key', 'aes');   which worked, but I am not able to decrypt the value. I inserted it in a field of datatype bytea but I'm not sure if that was the right way.   SELECT decrypt(pw, 'key', 'aes') FROM table WHERE ID = 1;   gives me the error     ERROR:  function decrypt(bytea, unknown, unknown) does not exist   LINE 1: SELECT decrypt(pw, 'key', 'aes') FROM tabelle WHERE ID = 7;                  ^   HINT:  No function matches the given name and argument types. You might need to add explicit type casts.   Does that really mean that encrypt() is an existing function, but not decrypt()? How else could I retreive aes-encrypted values?