How are new Stack Overflow ques always at the top of a google search
I'm just going to throw this out there, but Google indexes Stack Overflow really quickly
Implicit newline at the end of each paragraph? Evaluate the infinite product $$\lim_{ n\rightarrow\infty }\prod_{k=2}^{n}\left ( 1-\frac{1}{k^2} \right ).$$  I can't see anything in this limit , so help me please. Upgrade to the latest PHP version in Ubuntu I am using  in my server and NextCloud informs me that:     You are currently running PHP 7.0.32-0ubuntu0.16.04.1. Upgrade your   PHP version to take advantage of performance and security updates   provided by the PHP Group as soon as your distribution supports it.   So, I tried to upgrade me OS (Ubuntu 16.04), by executing:  apt-get update  apt-get dist-update  Then I restarted the server and I re-executed the above commands. After all these, when I connect from terminal I am getting:  Welcome to Ubuntu 16.04.5 LTS (GNU/Linux 4.4.0-83-generic x86_64)   * Documentation:  https://help.ubuntu.com  * Management:     https://landscape.canonical.com  * Support:        https://ubuntu.com/advantage  0 packages can be updated. 0 updates are security updates.   and my PHP version is still PHP 7.0.32-0ubuntu0.16.04.1 (cli) ( NTS ).  This means that PHP 7.0.32 is the latest possible version that I can install in ubuntu 16.04; Is this sentence grammatically correct?  Anyone who loves the English language should have a copy of this book in their bookcase.  or should it be:  Anyone who loves the English language should have a copy of this book in his or her bookcase. How can I enable access to USB devices within VirtualBox guests? I cannot see any USB devices within my VirtualBox guest VMs from my host. How do I enable access for my guest VMs?  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Function on $[a,b]$ that satisfies a Hölder condition of order $\alpha > 1 $ is constant I want to show that if a function $f:[a,b]\rightarrow \mathbb R$ satisfies a Hölder condition of order $\alpha &gt; 1 $ then it is constant.  The way I think of it is as follows:  $$|f(x) - f(y)| &lt; K|x-y|^\alpha$$  $$\frac{|f(x) - f(y)|} {|x-y]}  &lt; K|x-y|^{\alpha -1}$$  $$\lim_{y\rightarrow x} \frac{|f(x) - f(y)|} {|x-y]} \le \lim_{y\rightarrow x}  K|x-y|^{\alpha -1} =0 $$ As the limit is $0$, we can remove the modulus, so we get:  $$\lim_{y\rightarrow x} \frac{f(x) - f(y)} {x-y} = 0$$ So $f$ is derivable and $f'(x) = 0$ for all $x$ in $[a,b]$. Note that the reason we can add the limit $y\rightarrow x$ is because $[a,b]$ is closed in $\mathbb R$.  However, the question gives as a hint using the mean value theorem. I am not sure why one should do that. You would first have to prove that $f$ is derivable in a similar manner to what I did, and then prove that $f$ is constant. Or is there a simpler way to do it and I am missing it?  Also please inform me of any mistakes I did in the proof (if any)/ Thank you! How to make a bootable windows USB in Kali Linux I found this heart while exploring the crimson biome - what is it? Citing papers, that are cited within a paper? I am reading a paper which discussing the change in a specific idea in a field of science over time. I would like to basically summarize the points in the paper but in a smaller fashion by taking some quotes and explaining how they relate to my situation.   For instance, in the paper I am reading the author said "in 2002, Stanley and Miikkulainen [SM02b] argued that the topology of a neural network also affects their functionality" where the tag [SM02b] is a reference to a entry in the author's bibliography.   Is it sufficient to only cite the author of the paper, or do I need to cite both the author of the paper and the author of the paper the author cited in the paper? Is it possible to annotate equations (i.e. arrow signs/curly braces) to define each variable? I have quite a simple question. I was wondering if it was possible to do something like this in LaTeX:    But formatted a little more nicely.  It doesn't need to be arrows necessarily. Just some form of annotation marker. Could Tom Bombadil have defeated Sauron? Cleaning wax and pesticide from apple skin I am confused whether drift velocity depends upon area or not . I checked answers for this question but all of them were cancelling each other out . from the equation $$I = neAv$$ It is clear that drift velocity should depend upon area but at the same time don't you think that by increasing the area of cross section of a conductor should have resulted in increase in drift velocity please help me out with it in detailed answer of how should i go with all the possible cases and explanation ,thanks :) Fluent and Query Expression — Is there any benefit(s) of one over other? LINQ is one of the greatest improvements to .NET since generics and it saves me tons of time, and lines of code.  However, the fluent syntax seems to come much more natural to me than the query expression syntax.  var title = entries.Where(e =&gt; e.Approved)     .OrderBy(e =&gt; e.Rating).Select(e =&gt; e.Title)     .FirstOrDefault();  var query = (from e in entries              where e.Approved              orderby e.Rating              select e.Title).FirstOrDefault();   Is there any difference between the two or is there any particular benefit of one over other? Sort Array Elements (string with numbers), natural sort java.lang.IllegalArgumentException: The servlets named [X] and [Y] are both mapped to the url-pattern [/url] which is not permitted When should you use struct and not class in C#? My conceptual model is that structs are used in times when the item is merely a collection of value types.  A way to logically hold them all together into a cohesive whole.  I came across these rules :   A struct should represent a single value. A struct should have a memory footprint less than 16 bytes. A struct should not be changed after creation.   Do these rules work? What does a struct mean semantically? I'm learning calculus, specifically derivatives and applications of MVT, and need help with the following exercice:      Show that, for all $n &gt; 1$ $$\frac{1}{n + 1} &lt; \log(1 + \frac1n) &lt; \frac1n.$$    I tried to follow the below steps in order to prove the RHS inequality:   Proving that $f &lt; g$ on $I$ from $a$ to $b$:  Step $1$. Prove that $f' &lt; g'$ on $\operatorname{Int}(I)$.  Step $2$. Show that $f(a) \leq g(a)$ or that $f(a^+) \leq g(a^+)$  Following the above steps, let $f(x) = \log(1 + \frac1x)$ and $g(x) = \frac1x$, for all $x &gt; 1$. One has  $$f'(x) =  -\frac{1}{x^2 + x} \quad \text{and} \quad g'(x) = -\frac{1}{x^2}.$$  We note that, for every $x &gt; 1$, $f'(x) &gt; g'(x)$. Moreover, $f(1^+) = \log(2) &lt; 1 = g(1^+).$   My problem is that I got the wrong inequality sign in Step $1$.    Looking at the solution in my textbook, the author suggests using the MVT but I don't know how to apply it in this case. Convergence of a Harmonic Continued Fraction We have various ways of invoking apex. Triggers, Inbound Webservices, @InvocableMethod,@RemoteAction and what not. Often we call some or other utility methods from these execution contexts. I have some generic utility method,that should behave differently from the context it is called?  I know about Trigger.isExecuting but it only tells if its running in trigger context or not.  I have a utility method that creates lead from Webservices, VF button click and via Lightning . Whenever we create a lead I want some special operations to be done via the source it was originated.(Its not just updating a simple field leadSource, I have some methods that creates some childs and update other records of other type) . I can achieve this by passing an extra parameter to utility method to tell about source, but i have then to edit hundred of other class that uses this utility method. If i could dynamically find out via which context this piece of code is running,then i would have to change only one class to satisfy my requirement.    Is there something in APEX that tells in what context the apex method was called?