Prove that a function is differentiable at $x=0$
How to show that $f$ is differentiable at $x=0.$
We're using list view and details OnClick Javascript buttons which reference custom js ans css files stored in static resources and containing some shared logic/styles. The sample code below demonstrates how they are referenced.  {!REQUIRESCRIPT('/resource/CustomJQuery/js/jquery-1.10.2.js')}  {!REQUIRESCRIPT('/resource/CustomLib')}  $("head").append($("&lt;link rel='stylesheet' href='/resource/CustomJQuery/css/smoothness/jquery-ui-1.10.4.custom.css' type='text/css' media='screen' /&gt;"));   These files are also referenced in Visualforce pages.  Introduction of "Serve Static Resources from force.com domain" critical update breaking this way of using static resources in OnClick Javascript buttons - there is also Known Issue created for this .  So, my questions are:  1) Are there any ways to make it work with "Serve Static Resources from force.com domain" critical update activated. My assumptions for now are below, but they seem to be risky and may require significant changes:   hosting these js and css files on own server and referencing them in OnClick Javascript buttons and all other places; move to custom visualforce pages;   2) Does anyone know what's going on with "Serve Static Resources from force.com domain" critical update right now? It was scheduled in Winter 15 first, then it was postponed to Summer 15. Now it can't be found in any org in list of all critical updates at all. It has even disappeared from the list in orgs where it used to be 1-2 weeks ago.  3) How long Known Issue can be "In review" status, since related one has this status for more than 2 months?  Thank you Power Supply Capacity Formula Given that I am building a home computer from scratch and I have several components (MB, CPU, HDD, Video, Sound, etc) which have specific power requirements, is there a formula for me to calculate the size/capacity of the Power Supply I will need? I want to be able to expand the setup later on also... Why do we say that irreducible representation of Poincare group represents the one-particle state? Only because   Rep is unitary, so saves positive-definite norm (for possibility density), Casimir operators of the group have eigenvalues $m^{2}$ and $m^2s(s + 1)$, so characterizes mass and spin, and It is the representation of the global group of relativistic symmetry,    yes? Using Thunderbird and gmail, sent items appear as unread in "All Mail" I'm using a gmail account in Thunderbird. When I send a message, a new mail notification appears (sound and system try icon), an unread message appears in the gmail All Mail folder, and the account name turns blue.  I have to click on "Sent Mail" or "All Mail" to get rid of the notification. Unsubscribing from "All Mail" is not effective (it still turns the account name blue).  This seems to be popping up elsewhere (), but nobody has posted a helpful answer.  How do I keep Thunderbird from thinking that a sent message is new unread mail in the All Mail folder? Short story where a man discovers he's living in a fake world I may be conflating two separate short science-fiction stories here, so please bear with me. I definitely read this more than 10 years ago and it's likely to be older than that (60's, 70's?)    A man wakes up one day to discover that the world is subtly different. His wife acts strangely and there's a weird "groundhog day" vibe.    He discovers that his house is actually made entirely of painted metal, including things that should be wood (a boat that he made by hand, for example). He comments that in the real world, it's the fact that stuff doesn't work properly that shows you that you're living in reality (a wobbly doorhandle may have been mentioned?) He's constantly beset by advertising; brands of washing powder, political messages, etc. and people keep asking him what he thought about them. At one point, the advertisers start getting very aggressive, literally invading his house to dirty his clothes and driving around with megaphones to shout slurs about their political competitors. He finally breaks out of the town (with the assistance of his secretary?) and they discover that they're...      ...actually robots living in a simulated town used by advertisers to test slogans, etc.   The final twist is that...     ...the town fits onto a desktop and is encased in glass. Even if he could escape, he could never live in the real world since he's very tiny. What are the pieces of evidence that universe is expanding? How can I copy location info from geotagged phone images to images taken with my other camera around the same time? So i did quite a big trip recently, and took lots of pictures with my DSLR and occasionally Android phone. Only after coming back did i read about the whole GPX file, tracklog options in Lightroom. meaning i don't have such a tracklog file.  The android phone did geotag most photos it took. (at least, when it got a gps fix i guess)  So my question is, is there some software or way that will automatically copy the geotag from the android's photos to photos taken on the same time with my DSLR?  Or alternatively, generate a tracklog from the geotagged data in the android pictures? Our 21 month old toddler will use the potty when we leave her bottom bare - she has been successfully doing this for a month. Tired of cleaning stinky diapers, we leave her bottom bare when she is home.   She doesn't particularly enjoy wearing diapers, and when we put one on her, she doesn't take the initiative to tell us that she has to use the potty. However, when we have company over, we put a diaper on her.  We are trying to transition her into wearing panties; however, she is very opposed to them. She equates them with pants and doesn't want to wear them. While she is fully capable of dressing herself in pants, she hasn't mastered taking her pants off yet.   How do you introduce underwear to your child? When do people normally introduce underwear to their child? How do I explain the concept of having to take her panties off before using the potty?  We in no way want to discourage her use of the potty, as she seems to really enjoy pooing/peeing outside (she claps for herself whenever she uses the potty). But if she is interested in potty training herself, I do want to show her the concept of an underwear. There is no continuous injective function $f:\mathbb{R}^n\longrightarrow\mathbb{R}^m$ Quantum Field Theory without LSZ, how is it possible? $\lim_{h\to 0}\int \frac{f(x+h)-f(x)}{h}\,\mathrm{d}x = f(b)-f(a)$ Let $f:[a,b]\to  R$ be integrable and continuous on $(a,b)$. Prove that: $$\lim_{h\to 0} \int_a^b\frac{f(x+h)-f(x)}{h} \,\mathrm{d}x = f(b)-f(a).$$  What I've tried so far: make a change of variables, which didn't help. I also thought of using the intermediate value theorem inside the integral, but the function being differentiable is not specified. Any help, tips? Thanks in advance! We were discussing Kirchoff's theorem on blackbody radiation in class today and the equation was: $$e_{f}= J(f,T)$$  $e_f$ was defined as power per unit area per unit frequency. What does per unit frequency refer to here? I know what per unit time means but don't understand 'per unit frequency'. Why does the Community user sometimes approve or reject edits? How does a machine know if my edit is valid? What does it mean if my edit was rejected by Community?     See also: What areas of physics depend on the sum $1 + 2 + 3 + 4 + 5 + 6+ 7+\ldots= -1/12$? This youtube video from Numberphile,   shows how the value is derived. In the video, one interviewee claims that "this result is used in many areas of physics". In the video, only string theory is mentioned.  Which areas of physics use or depend on the sum $$1 + 2 + 3 + 4 + 5 + 6+ 7+\ldots= -1/12?$$ How to prove that $\lim\limits_{h \to 0} \frac{a^h - 1}{h} = \ln a$ In order to find the derivative of a exponential function, on its general form $a^x$ by the definition, I used limits.  $\begin{align*} \frac{d}{dx} a^x &amp; = \lim_{h \to 0} \left [ \frac{a^{x+h}-a^x}{h} \right ]\\  \\ &amp; =\lim_{h \to 0} \left [ \frac{a^x \cdot a^h-a^x}{h} \right ] \\  \\  &amp;=\lim_{h \to 0} \left [ \frac{a^x \cdot (a^h-1)}{h} \right ] \\  \\ &amp;=a^x \cdot \lim_{h \to 0} \left [\frac {a^h-1}{h} \right ] \end{align*}$  I know that this last limit is equal to $\ln(a)$ but how can I prove it by using basic Algebra and Exponential and Logarithms properties? Thanks How do I replace multiple spaces with a single space in C#? How can I replace multiple spaces in a string with only one space in C#?  Example:  1 2 3  4    5   would be:  1 2 3 4 5 So far I've been using public void run() {} methods to execute my code in Java. When/why might one want to use main() or init() instead of run()? Detection of the Electric Charge of a Black Hole By the "No Hair Theorem", three quantities "define" a black hole; Mass, Angular Momentum, and Charge. The first is easy enough to determine, look at the radius of the event horizon and you can use the Schwarzschild formula to compute the mass. Angular Momentum can be found using the cool little ergosphere Penrose "discovered". However, I don't know how to determine the charge of the black hole.   How can an electromagnetic field escape the event horizon of a Reissner-Nordström black hole? Is there any experiment we could theoretically do to a black hole to determine its charge? How can I reset my Ability Points? I'm also curious about being able to reset my points, should I wish to change my ability configuration later.  So far (10h-ish) I've only seen one way, which is a potion sold by Kiera Metz for 1000g. However she's no longer available as a store, due to a story choice, so I'm not sure where else I could buy this potion.  Where might I buy this potion, and is it the only way to reset your ability points? Unsealed meat in freezer Below is my situation:  Is completely (vacuum) sealing leftover meat in the freezer absolutely necessary? I would always just use a plastic bag to cover the meat and fold it around couple of times so it's almost as good as sealed (usually grocery plastic bag is much bigger than the piece of meat) and have never had a problem with it last a decade or so I have been cooking.  But recently I got this new roommate who insists on me using special small plastic bags with sealers to use and he is being very paranoid, obsessive about it.  So my question is: Is he right?