What is a single word for someone who is easily discouraged?
How can you describe someone who gives up too easily?
Prove that the derivative of $x^w$ is $w x^{w-1}$ for real $w$ Can anyone give a proof of the derivative of this type of function? Specifically showing that  $\dfrac{d(x^w)}{dx} = wx^{w-1}$ for a real $w$?  I tried to use the Taylor series expansion for $(x+dx)^w$ and got the correct result. However, the proof of the Taylor series requires knowledge of the derivative of these functions. So this is essentially circular reasoning. I know that the same series is also given by the binomial expansion, but that's not entirely satisfactory either, because where's the proof that the binomial expansion works for all reals (isn't it only apparent for integers)? So far all of the arguments I've come across involve circular reasoning. I was thinking of showing that the binomial expansion is true for all reals using some form of proof by induction e.g. something like this.  I'm really not sure. Align multiline equation with expression after equal sign I am trying to align a multiline equation using array within the equation but it turns out it doesn't do very well. The code I am using is as follows:  \begin{equation}    \begin{array}{lcl} \mathcal{L}^{-1}\left\{f(d)\right\} &amp;= \mathcal{L}^{-1}\left\{f_1(\delta).f_2(\delta)\right\} \\ &amp; = exp(mt) \star \left\{\frac{l}{2\sqrt{\pi t^3}} exp(-l^2/{4t})\right\} \\ &amp; = F_1 * F_2 \end{array} \end{equation}   Can anyone suggest better way to deal with it ? XML - Data At Root Level is Invalid How can we prove that $D(f)\backsimeq\operatorname{Spec} A_f$? Let $$D(f)=\operatorname{Spec}A - V(f)=\{p\in \operatorname{Spec} A:f\notin p\}$$ be the principal open subsets of $\operatorname{Spec}A$ with the Zariski topology. I'm trying to prove that $D(f)\backsimeq \operatorname{Spec} A_f$, where $A_f$ is the localization of $A$ at $f$.  If we consider the canonical homomorphism $\varphi:A\to A_f$ given by $\varphi (a) = \frac {a}{1}$, we can define $\varphi':\operatorname{Spec} A_f\to \operatorname{Spec} A$, given by $\varphi'(p)=\varphi^{-1}(p),\forall p\in \operatorname{Spec}A_f$.  I'm having trouble proving that this map is surjective.  Thanks. Is the unit sphere in $\Bbb R^4$ path connected? What is the daily reputation cap and how can I hit it? I've found some questions and those two badges "Epic" and "Legendary" regarding the "daily reputation cap". What is it and how can I hit it? Custom Gmail labels sort I want to sort the labels in my own order instead of the default abc order, so that, for example, the label named bills should come up first.  Any way to do that? I once saw watch a sci-fi movie or an episode of a tv series (not sure) in which:   Every police officer was a judge, and hence could act by themselves on the streets. Each "judge" had a gun, which appended their DNA to the bullet. This was used later in investigations about a crime scene, and I think was confidential before the trial was held. Only a judge could use the gun, try to use it and you've been electrified. Also the guns had a self-destruction feature. The main villain was an ex-judge who purchased and activated a very old "killer robot" which was a residue of a long-ended war. When a judge was exiled, they were given a copy of the book of law, and sent outside the city to enlighten the people outside cities.   Can you help me find it?  PS: It was difficult to select a title How can i integrate one SFDC org to another SFDC using Rest Api I am trying to integrate one Salesforce org to other org by using Oauth setup, I wanted to use  use consumer key and consumer secret key in my REST class to connect with the org, after connection part completion, I want to access Get(), Put(), Post(), etc. Including the ability to set Oauth and Authorization headers needed for Salesforce Rest API calls.  Actually I'm new in REST implementation so can you please explain me by using code samples. How to place an image at the right top of a document? I've been learning LaTeX and this community has been very helpful. Currently, I'm trying to set up corporate letters but as a newbie I'm encountering a  of , so I'm posting them one by one instead of putting it in the comments... maybe this helps others as well.  Anyway, I am trying to implement this  that indicates that I can use vbox to float an image to the right of my header. I almost have this working, but I now try to adjust this to get my logo to stick to the top of the page. So I want to have this at the right top of my document. This is quite difficult! When I place the vbox, it creates unwanted spacing, for some odd reason. So I can not get the logo to be at the right top, even though I 'reset' every possible margin to 0 (in my opinion). Here is my distilled code:  \documentclass[a4paper]{article} \usepackage{graphicx} \graphicspath{{./img/}} \usepackage{color} \usepackage{xcolor} \definecolor{orange}{HTML}{DD4616} \definecolor{white}{HTML}{FFFFFF} \usepackage{fullpage} \usepackage[margin=0cm, paperwidth=215.9mm, paperheight=30mm,top=0cm]{geometry} \parindent=0pt  \begin{document} \fboxsep0pt  \pagecolor{orange}   \fbox{\vbox to 0pt{\hfill\fbox{\includegraphics[height=3cm]{logo}}}}  \end{document}   I've used a full black logo for illustrative purposes. Here you can see this:    The black line is the vbox border. For some reason, it jumps down. The only way to get rid of this that I found out about is this:    Which means that I need to add:  \edef\theprevdepth{\the\prevdepth}\nointerlineskip \vbox to 0pt{...}\prevdepth=\theprevdepth   But there are two problems with this:   I get an error with I try this (Improper \prevdepth.) More importantly, I really want to understand my code at this point, and get to master the basics of positioning elements. This feels overcomplicated and I do not understand it at all.    Is there any easy way to position an image at the right top of a document? Show that if $u$ is harmonic in $\mathbb R^n$ and $u=o(|x|)$, then $u$ is a constant.(Hint: use the solid version of the mean value property $u(x)=\frac{1}{\omega R^n} \int _{B_{R(x)}} u(y)dy$, and estimate $|u(x)-u(x')|$.)  Can anyone tell me how to use this hint? Can I get a postdoc in China more than 3 years after having received my PhD? Contour integral of $\sqrt{z^2-1}$ on $|z| = 2$ I've been wrestling with this problem (available  ):  Evaluate the integral of $f(z) = \sqrt{z^2-1}$ around the circle $\{z: |z| = 2\}$, where the branch of the square root function is chosen so that $\sqrt{2^2-1} &gt; 0$.  I came up with the answer $$\int\limits_{|z| = 2} \sqrt{z^2-1} dz = \pi i$$ using the following argument, which seems a little like voodoo to me.  You notice that there are two points, at $z \pm 1$, where you might have to pick a branch of $log()$ to define the square root. Then, I convinced myself that as long as you exclude from your domain the real interval $-1 \le x \le 1$, the function $f(z)$ can be continuously defined (maybe the two branches somehow cancel?), and so is analytic on its domain.  Therefore you can shrink the contour of integration continuously using the Cauchy Closed Curve Integral Theorem, so that you wind up reducing it to the real integral $$2\int_{-1}^1 \sqrt{x^2-1} dx = \pi i$$  I'm not really sure the answer is correct, and I'm even less certain about the way I got it. I had a hard time convincing myself that $\sqrt{z^2-1}$ was not multi-valued on the domain. To try to get at that I tried $\sqrt{z^2-1} = \sqrt{z+1} \sqrt{z-1}$ and reasoned that the product makes the discontinuity disappear, using $$e^{\frac{\pi}{2}i}\cdot e^{\frac{\pi}{2}i} = -1 = e^{-\frac{\pi}{2}i}\cdot e^{-\frac{\pi}{2}i} $$ for the different branches of $log()$ you can choose.  I'd appreciate any input that would help me get a a better way to look at this.  Thanks!    EDIT  An attempt to use the Residue at infinity:  By substituting $z = 1/w$ you get \begin{eqnarray} \int\limits_{|z| = 2} \sqrt{z^2-1} dz &amp;=&amp; \int\limits_{|w| = 1/2} \frac{1}{w^2}\sqrt{\frac{1}{w^2}-1} dw \\ &amp;=&amp; \int\limits_{|w| = 1/2} \frac{1}{w^2}\sqrt{\frac{1-w^2}{w^2}} dw \\ &amp;=&amp; \int\limits_{|w| = 1/2} \frac{1}{w^3}\sqrt{1-w^2} dw \end{eqnarray} The integrand is analytic in $|w| \le 1/2$ except at $w = 0$, so we can apply the Residue Theorem. Near $w = 0$, $\sqrt{1-w^2} = 1 - \frac{1}{2}w^2 + \dots$, so the residue of $\frac{1}{w^3}\sqrt{1-w^2} $ at $w = 0$ is $-\frac{1}{2}$. Then the integral is $$\int\limits_{|z| = 2} \sqrt{z^2-1} dz = 2\pi i \cdot (-1/2) = -\pi i$$ My inline-block elements are not lining up properly I'm new to Linux (currently running Ubuntu 10.04) and I have just finished setting up SSH access to my Linux Machine.  Currently, I have to use ssh root@x.x.x.x to connect but would much rather be able to swap the IP for the computer name (like in Windows with \\name) or a domain name (like computername.example.com). I don't really know where to start so any help would be most appreciated.  Please go slowly, as mentioned - I am still new to this.  EDIT 1 Completely forgot to mention that I am trying to connect from Windows 7 (via PuTTY) - sorry. Is it possible for a foreigner to drive through (mainland) China in a foreign-registered car? Is it possible to drive through mainland China, for example for transit from Kazakhstan to Vietnam, as a non-Chinese citizen, in an own car/van/truck?  This is about an European Union citizen, trying to make a tourist trip overland by car from the EU to Vietnam. This is about a special (equipped with sleeping, cooking and other facilities) vehicle, that the owner intends to keep and use in Vietnam, so buying/renting a vehicle inside China and selling it before leaving is not an option - the question is about driving a specific vehicle the owner already has in the EU to Vietnam. getting new licence plates is OK, as long as it is allowed to put back the old ones when the vehicle gets back to the EU.  What legal issues are there with getting in an own car over China, and how to overcome them?  Is it possible to drive a car with EU licence plates through China, or would one have to get something like temporary Chinese plates? Is an EU driving licence valid? Are there any customs issues one has to know about, and how long one can keep a foreign motor vehicle in China without having to pay import taxes on it? Dealing with a whole bunch of two-line config files, I'd like a way to exclude any files that have a different number of lines.  So, something like:  mv * destdir only if file contains exactly two lines   Or:  wc -l * | grep '^ *2' | xargs mv {} destdir   Except that neither of those is actual working code.  While writing this I realized I do have a way to do this, which is ugly as heck, and I've included it below as an answer.  Is there an easy/clean way to do this? What constitutes an observation/measurement in QM? Fundamental notions of QM have to do with observation, a major example being The Uncertainty Principle.    What is the technical definition of an observation/?  If I look at a QM system, it will collapse. But how is that any different from a bunch of matter "looking" at the same system?  Can the system tell the difference between a person's eyes and the bunch of matter?  If not, how can the system remain QM?  Am I on the right track? Can I make a custom node from a group and have that available in other projects? I've found some neat combinations of nodes to create certain effects, so I'd like to make them a group and then have that node available on my list of available nodes, even when I reload the startup file. How would I do that? Hi this must be a basic question but I haven't seen an answer with cerbot considerations (if there are any considerations). How do I get https www to redirect to non-www instead of timing out?  The https www version of my site times out instead of redirecting to non-www, whereas all other versions (http and https non-www) work fine.  Preferably I would like to future proof so that I can renew the certs through certbot and not need to manually change the nginx config afterwards.  The nginx server config is shown below:  server {     listen 80 default_server;     listen [::]:80 default_server ipv6only=on;     server_name www.mydomain.com mydomain.com;      listen 443 ssl; # managed by Certbot     ssl_certificate &lt;path_to_cert&gt; # managed by Certbot     ssl_certificate_key &lt;path_to_key&gt;; # managed by Certbot     include /etc/letsencrypt/options-ssl-nginx.conf; # managed by Certbot     ssl_dhparam &lt;path_to_this&gt;      if ($scheme != "https") {         return 301 https://$host$request_uri;     } # managed by Certbot }