How do I show that this function is continuous?
the cone is contractible
Calculating slope in percentage with QGIS I'm working with QGIS, v. 2.0.1. I have several soil types. They are (amongst others) described with slope indications. I already calculated the slope from the DTM in degrees, but as description of the soil types is in percentage, I need to calculate the slope in percentage. I tried two things:  I tried the analysis tool from the raster section, but it didn't work. The result was just black with values from 0 to 0. The same happened when I tried to calculate the percentage in the raster calculator but the result was the same.  Maybe I need to say that the terrain is pretty plain. What else can I do? Update I tried the raster calculator and did what @radouxju suggested. It gave me a black picture with values from 1756.64 to 1756.64. But as soon as I click in the picture the values are &quot;normal&quot;, say 5.88 or 13.224 or something like that. The same happens when I try the gdaldem tool but with values from 0 to 0. I also tried to change the contrast enhancement (like stretch to min/max) but it didn't change anything. Update 2 I just  that maybe I have to set the scale to 111120  but that doesn't work neither (result: black, values 0-0). Vertex cover in a graph with maximum degree of 3 and average degree of 2. when upgrading to a 200 amp service panel with service drop coming from bottom underground do I need southern California Edison to come disconnect and then reconnect or can I just do it on my own. I do have a permit. How to blacklist kernel modules? How do I disable loading of unnecessary kernel modules. Kernel 3.2.4 I would like to know how to upgrade from my current version of Ubuntu to the next stable from the Command line interface? $P(X<Y)$ where X and Y are exponential with means $2$ and $1$ $P[X=x]=0$ when $X$ is continuous variable I know that for continuous variable $P[X=x]=0$.   But i can't visualize that if $P[X=x]=0$, there is infinite number of possible $x$'s. And also why do their probabilities get infinitely small ? Allowing FTP access to a local user without allowing SSH/command line access Priority and timing between enchantments and instants If I have priority and cast an  on a just summoned 2/3 creature, then, passing priority, my opponent casts a  on that creature, does my creature survive? The first spell that resolves is obviously the bolt, that deals 3 point of damage to the creature; but immediately after, will the  Unholy Strength resolve (giving +2/+1), allowing the creature to survive? Prove that the function $f(x)=\frac{x}{x^2+1}$ is continuous at $x=-1$. Prove  that the function $\displaystyle f(x)=\frac{x}{x^2+1}$ is continuous at $x=-1$. You should give a proof that is directly based on the  definition of continuity.   I saw many similar questions on this website, but none of them gave me a satisfactory answer. I more or less understand how epsilon-delta proofs work but my problem lies more in the algebraic manipulations probably. So here's my "attempt".  Definition of continuity; for $f:A \to \mathbb{R}$     $$\forall \varepsilon &gt;0 \ \exists\delta&gt;0\ \forall x \forall x_0 \in A:|x-x_0|&lt;\delta \Rightarrow |f(x)-f(x_0)|&lt;\varepsilon$$   So from what I understand, the procedure for epsilon-delta proofs are as follows: 1. Plug the point of interest $x_0$ into $|f(x)-f(x_0)|&lt;\varepsilon$ 2. Write $x$ in terms of $\varepsilon$ 3. Then plug $x$ into $|x-x_0|&lt;\delta$ 4. Find $\delta$ in terms of $\varepsilon$. Done    At step 1, we have $\left|\dfrac{x}{x^2+1}+\dfrac{1}{2}\right|&lt;\varepsilon$. Step 2 is where I'm stuck because of the 2nd degree polynomial in the denominator. First, I did this: $\left|\dfrac{x}{x^2+1}\right|&lt;\left|\dfrac{x}{x^2+1}+\dfrac{1}{2}\right|&lt;\varepsilon$. Then, I wasn't too sure about what to do, I thought about getting rid of the "$1$", but that would screw up my inequality. I thought about factoring $x^2+1$, but it doesn't have any real roots. I tried inverting the fraction, but that led me to nowhere. And I've already exhausted the tools I have. How do I proceed?  Apparently, epsilon-delta proofs are the most basic building blocks of analysis. And I'm already failing, this is both embarrassing and depressing... I am in trouble with polarization and entanglement. Let's consider three cases : Case 1) : Statistical mixture of $|H\rangle$ and $|V\rangle$ polarized photons Case 2) : Photons in a superposition state $1/\sqrt{2}(|H\rangle+|V\rangle)$ Case 3) : Photons which are entangled with twin ones in $1/\sqrt{2}(|H,H\rangle+|V,V\rangle)$ state Which experiments can be conducted to differentiate the case  statistical mixture from the case  superposition state ?   Which experiments can be conducted to differentiate the case  statistical mixture from the case  entangled photons in superposition state ?   Using a $45^\circ$ polarizer I think you can differentiate case 1/case 2 but not case 1/case 3 I don't know how to differentiate case 1/case 3 except maybe using quantic tomography and Wigner function. Is it true ? Is there any other simpler way ? Thanks a lot for your answer and sorry for this maybe dummy question... Singular or plural verb form where subject includes a "parenthetical" element My question arises from , where OP asks whether he should use the singular or plural verb form after "the title, as well as the tone,"  As luck would have it, when I searched Google Books for , I found...        ...and...        At the risk of having this question closed as just peeving, I feel that the first one should have been plural "err", because without the commas it seems to me both "the title" and "the tone" have more or less equal status as "joint" subjects of the verb, making it plural.  On the other hand, I feel the commas in the second example effectively demote "the tone" to "parenthetical" status (the clause is almost incidental). Since this encourages us think of "the title" as the primary subject, it should have been singular "derives".  I'm no great fan of "grammatical rules", but it seems weird to me that the only two relevant examples for this specific wording should both (in opposite ways!) contradict my inclinations.  What's going on? i was stopped by my sister from upgrading Ubuntu, for the reason she explained was that i would have to reinstall all the softwares that I've installed in last 6 months. but i think if that's the case, the upgrade itself includes all softwares that i have installed. so please tell me what's the truth?     please note that i just can't afford mentally to reinstall all apps due to slow INTERNET speed.because it may take 3 to 4 days of constant downloading.   if you are an Indian living in an suburban city,you can understand my situation.   i think the question itself explains everything.still I'll explain everything in detail.i want to upgrade my current Ubuntu 12.10 OS to 13.10(now please don't ask what is 13.10). this option is available from "about this computer" and many other places.the upgrade is of about 700mb to 800 MB.    BTW, i don't know why i think it's a rule here to put some question on questions asked here,however detailed or/and simple it may be.at least that's what i feel after looking at many questions. How can I get sql string, generated by Linq2SQL ORM? I want to crop (as in, take a subset of each frame, like when you crop a photo) a video in Windows Live Movie maker. Is there a way to do this, and failing that is there another free tool i can use to do that? See code:   var file1 = "50.xsl"; var file2 = "30.doc"; getFileExtension(file1); //returns xsl getFileExtension(file2); //returns doc  function getFileExtension(filename) {     /*TODO*/ } Is there a way to set transparency of windows in GNOME? "Arnold raced out of the door": grammatical or not? Two ethernet ports on motherboard. How can I get double the bandwidth? Direct Question:  My evga classified motherboard has two ethernet ports.  I want to use them simultaneously to improve the speed of a remote connection.  (Yay for programming remotely).  How do I do this?  At present /etc/network/interfaces:  auto lo eth0 eth1  iface lo inet loopback  iface eth0 inet static address 192.168.1.202 netmask 255.255.255.0 gateway 192.168.1.2  ifrace eth1 inet static address 192.168.1.201 netmask 255.255.255.0   What should I change? Is there a package I need to install to bond the two channels.  Background: I do a lot of remote computing both from home to office and office to home.  But (to take my ISP out of the equation), let's frame the question as if I'm really just interested in maximizing the file transfer rate between two computers on the same (local) network.  Both boxes have dual ethernet motherboards.  Using a simple Linksys WRT54GS as a 5 port switch (ignore wireless and isp) -- how do I maximize the transfer rates between the computers?  Please Note: I'm not interested in load balancing -- Correct me if I'm wrong, but I want to bond the two channels together so that the box appears as if it has one connection that's twice as fast. On really old Ubuntu 6.06 - How to upgrade