How to view the v8 javascript stack?
How to set a JavaScript breakpoint from code in Chrome?
Show that $\left | \sin a - \sin b \right | \leq \left | a-b \right |$ My mother is given a UK tourist visa for 2 years with a duration of stay as 180 days. It is a c type multiple entry visa. Is this 180 days is the total stay she can take or is it duration of stay per visit.  Thanks in advance for your reply. mkdir -p will create a directory; it will also make parent directories as needed.  Does a similar command exist for files, that will create a file and parent directories as needed? Does an Action Surge grant a second bonus action? We were trying to understand how the "Action Surge" rule works, and after some discussion we came to a standstill.      Starting at 2nd level, you can push yourself beyond your normal limits for a moment. On your turn, you can take one additional action on top of your regular action and a possible bonus action   The keyword "possible" is what threw us off. Half the group thought it meant "additional action or bonus action", and the other half thought it was "additional action and bonus action".  So which is it? Finding the radius of convergence for $\sum_{n=0}^{\infty} \frac{(n!)^kx^n}{(kn)!}$ I'm reviewing some calculus concepts right now, and this series stumped me. I'm trying to figure out what its radius of convergence is, but it's not falling for any of my old tricks. Using the root-test, I want to compute: $$ L_1=\lim_{n\rightarrow\infty} \left|\sqrt[n]{\frac{(n!)^k}{(kn)!}}\right| $$  where $k$ is some positive integer. Passing the limit through the absolute-value bars and $n$th root symbol, I now want to compute the simpler (?) $$ L_2 = \lim_{n\rightarrow\infty} \sqrt[n]{\frac{(n!)^k}{(kn)!}}$$  Which I can't seem to pin down. Numerical tests indicate it goes to 0, and that jives with an intuitive notion I have that there are always $k$ terms on the numerator, but $kn$ terms in the denominator. But since all of these terms themselves depend on $n$, proving that $L_2 = 0$ escapes me. Once we get this result (if it's correct), then clearly $L_1$ is also 0, and the radius of convergence of the series is $\mathbb{R}$. Thanks for any ideas you may have. Which features of a wizard's familiar, if any, are considered magical? The  spell has a duration of instantaneous, which implies that the familiar itself is not an ongoing magical effect. However, the spell provides a number of ongoing features that are definitely supernatural:    The familiar disappears when it drops to 0 HP. The wizard can temporarily or permanently dismiss the familiar. The wizard can communicate with the familiar telepathically. The wizard can observe through the familiar's eyes and ears. The familiar can deliver touch spells on behalf of the wizard.   Which of these features are considered magical? For example, would any of them show up to a detect magic spell or be suppressed by an antimagic field? In addition, is my assumption above correct that the familiar itself is not considered magical? Contraction of quotient ideal is quotient of contractions? I've been modeling an F-15, but when I rotate the flaps on Y-Axis the Flaps offset from the wing and they look like they are about to fall out, so I end up correcting it by rotating in the X and Z-axis to align them correctly.  However when I rotate them back from the Y-Axis they look distorted again because I did rotations on the X and Z axis. I tried riding it, no help. I saw something about custom orientation to fix it but that was not clearly explained and it was done on an ideal plane that was (0,0,0); mine is pre-rotated on all axis.   I'll take scripts if needed and I'm using Blender 2.8.  When I rotate it on the Y-Axis:    Fixing it using X and Z rotation:    Rotating it back on the Y distorted it again:    Here's the wing with ailerons and flaps: DropDown list onchange event and AJAX in MVC The uniform limit of Continuous Functions is continuous.   Proof Let $\varepsilon &gt; 0$. There exists $N$ in natural numbers such that $n&gt;N$ implies  $|f_n(x)-f(x)| &lt; \frac{\varepsilon}{3}$ for all $x$ in $S$. In particular $|f_{N+1}(x)-f(x)| &lt; \frac{\varepsilon}{3}$ for all $x$ in $S$. Since $f_{N+1}$ is continuous at $x_0$ there is a $\delta&gt;0$ such that, $x$ in $S$ and $|x-x_0| &lt; \delta$ imply $|f_{N+1}(x)-f_{N+1}(x_0)|&lt; \frac{\varepsilon}{3}$ Now we conclude $x$ in $S$ and $|x-x_0| &lt; \delta$ imply $|f(x)-f(x_0)|&lt; 3 \cdot \frac{\varepsilon}{3} = \varepsilon$.  Can someone explain what is happening here? I don't follow it all. Professionals: Would you choose GIMP over Photoshop and/or Inkscape over Illustrator? How to Understand the Definition of Cardinal Exponentiation I'm having trouble understanding the definition of cardinal exponentiation.  Let's start with the definitions / claims I've been given:  For any finite sets $A,B$, such that if $|A|=a$ and $|B|=b\neq 0$ then the number of functions from $A$ to $B$ is $b^a$. ( I'm guessing this is only used when both sets are finite ).  For any sets $A,B$, $B^A$ is the set of functions from $A$ to $B$.  For every set $A$, $|P(A)|=|\left \{ 0,1 \right \}^A|$  Now for the definition and why I don't understand it:  Let $a,b$ be cardinal numbers.  Let $A,B$ be sets such that $|A|=a, |B|=b$.  Then $|B^A|=b^a$.  How analagous to normal exponentiation is this and where does in differ when we introduce cardinals like $\aleph_0$ or $C$?  Is $2^2=4$ and is $\frak c^2=c\cdot c=c\times c$? Why does my pilot light keep going out? My furnace pilot light keeps going out so I changed the thermocouple. Now the furnace will come on and heat up to the degree set on my thermostat, then the pilot light will go out and the furnace will not come back on.    Could the thermostat be bad and cause the pilot light to go out? What's the name of this flat illustration style? I want to buy some stock photos like the ones below. What is this design called?  I don't even know how to start searching... Why is the first band on a resistor never black? I'm taking an electronic circuit analysis class, and I was asked to give the color of the 3rd band of a 1MΩ resistor. My answer was blue, thinking it could be black-brown-blue (01 * 1MΩ), but the automated quiz said the correct answer was green (brown-black-green).  So I did some research, thinking there were just multiple correct answers, and I read in a few places that the first band on a resistor is never black (0). Why is this? Does a black first band have some other meaning? It would really help me remember it if I knew the history or reasoning behind it.  This question has been answered. For further reading on zero-ohm resistors mentioned in the answers and comments here, I found these questions and answers helpful: Multiple "order by" in LINQ I have two tables, movies and categories, and I get an ordered list by categoryID first and then by Name.  The movie table has three columns ID, Name and CategoryID. The category table has two columns ID and Name.  I tried something like the following, but it didn't work.  var movies = _db.Movies.OrderBy( m =&gt; { m.CategoryID, m.Name }) How to calculate the sum of sequence $$\frac{1}{\binom{n}{1}}+\frac{1}{\binom{n}{2}}+\frac{1}{\binom{n}{3}}+\cdots+\frac{1}{\binom{n}{n}}=？$$ How about its limit? Are both try to save the file and try saving the file grammatically correct? If so, is there any difference in meaning? What conditions are necessary for a Wither Skeleton to spawn naturally, and can I manipulate those conditions to increase the chance of them spawning?  I want to make a Wither Skeleton spawning pad in the Nether but I'm having trouble finding Wither Skeletons. I've only heard that they spawn in Nether Fortresses. Point Release upgrade from 14.04.1 to 14.04.2? I wanted to upgrade to 14.04.2 point release from 14.04.  What I did was:  sudo apt-get update &amp;&amp; sudo apt-get upgrade &amp;&amp;  sudo apt-get dist-upgrade -y   Then I wanted to upgrade to 3.16 kernel, since it wasn't done with the the above command, so what I did was:  sudo apt-get install linux-generic-lts-utopic xserver-xorg-lts-utopic libegl1-mesa-drivers-lts-utopic xserver-xorg-video-all-lts-utopic xserver-xorg-input-all-lts-utopic sudo apt-get install linux-signed-generic-lts-utopic   Now when I do:   uname -a I get   Linux Y500 3.16.0-33-generic #44~14.04.1-Ubuntu SMP Fri Mar 13 10:33:29 UTC 2015 x86_64 x86_64 x86_64 GNU/Linux  cat /etc/os-release | grep VERSION= I get  VERSION="14.04.2 LTS, Trusty Tahr"   And when I do lsb_release -a I get  Distributor ID: Ubuntu Description:    Ubuntu 14.04.2 LTS Release:    14.04 Codename:   trusty   I know that uname -a and lsb_release -a both refer to different info, but why does  cat /etc/os-release | grep VERSION= show different version?