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(I'm aware of  but it has no answers…)  Let be $u_0 \in \mathbb{R}$ and the sequence $(u_n)_n$ defined by: $u_{n + 1} = \frac12 \arctan(u_n)$.  I define also: $v_n = 2^n u_n$, so I can show that: $\lim (u_n)_n = 0$ (by studying $x \mapsto \frac12 \arctan(x)$), thus, I can show that $(v_n)_n$ is monotone and converges because it is bound.  Now, I conclude: $u_n \sim \dfrac{l}{2^n}$, I'd like to determine $l$ more precisely.  Here is what I tried, I suspect $l$ to be something like $f(\pi)$ for some $f$ :   push the asymptotic expansion of $\arctan$ to the 2nd order and reinject it ; use $\arctan(u_n) + \arctan(1/u_n) = \dfrac{\pi}{2}$ ; use series techniques to look for $\sum v_{n + 1} - v_n$, maybe conclude using Cesaro summation Is $|xy|$ differentiable in $(0,0)$? Is $f(x,y) = |xy|$ differentiable in $(0,0)$? I have no idea how to approach this problem. Is it possible to check out subdirectories of a repository in Git?  Imagine I am setting up a new WordPress installation. I will create two new directories for my plugin and theme customization:   wordpress/wp-content/plugins/myplugins/  wordpress/wp-content/themes/mytheme/   I want to maintain these directories via Git. In Subversion, I would accomplish this by having trunk/myplugins/ and trunk/mytheme/ directories and checking out subdirectories. Does Git have a way to accomplish the same task using a single repository?  I could just be missing the boat on some Git paradigm, as a long time SVN user with little exposure to Git.  Edit:  storing different content is an interesting way to handle this. I was wondering if it is possible to get a link to a rigorous proof that  $$\displaystyle \lim_{n\to\infty} \left(1+\frac {x}{n}\right)^n=\exp x$$ How precisely do I need to post close to 7:00 (somewhere) to get hero of time? Using first person or third person in papers? Volume of $T_n=\{x_i\ge0:x_1+\cdots+x_n\le1\}$ Let $T_n=\{x_i\ge0:x_1+\cdots+x_n\le1\}$. I know $T_n$ is tetrahedron.  My question: How can I compute the volume of $T_n$ for every $n$? How to check whether a JavaScript variable defined in cross-browser way?  I ran into this problem when writing some JavaScript utilizing FireBug logging. I wrote some code like below:  function profileRun(f) {     // f: functions to be profiled     console.profile(f.constructor);     f();     console.profileEnd(f.constructor); }   It works fine in FireFox/FireBug, but it reports error in IE8 RC1. So, I'd like to do some checking whether console variable exists in the execution environment.  Below code works fine in FireFox, but not in IE8 RC1.   function profileRun(f) {     if (console != undefined) {         console.profile(f.constructor);     }      f();      if (console != undefined) {         console.profileEnd(f.constructor);     } }   However, if I do it this way. It works in IE8 RC1. 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The equivalent electric field of a magnetic field I know that Lorentz force for a charge $q$, with velocity $\vec{v}$ in magnetic field $\vec{B}$ is given by  $$\vec{F} =q \vec{v} \times \vec{B}$$  but there will exist a frame of reference where observer move at same velocity with that of charge $q$, so according to him $v=0$. hence he will see no magnetic force is exerted on charge $q$. I have work on this problem for a while and found that the special relativity predicts equivalent electric force will acting upon charge instead. I want to know the relationship between this equivalent electric force and magnetic force.  Thanks in advance "It really doesn't matter" v "It doesn't really matter" Why is "No new release found" when upgrading from a LTS to the next? Play Framework (2.1.3) doesn't run any tests How to compute $\,3^{3^{3^{\:\!\phantom{}^{.^{.^.}}}}}\!\!\!\!\bmod 46,$ for power tower height $2020$? What is the remainder of $\,3^{3^{3^{\:\!\phantom{}^{.^{.^.}}}}}\!\!\!$ divided by $46$?  The level of powers is $2020$.  First there is no parenthesis so it means 3 power of 3 which is also power 3 and so on 2020 times  Second I think that we can use Fermat's Little Theorem but I don't know how, and maybe there is a better way. How can I delete my account? How can I delete my Stack Exchange account(s)? Also,  What happens to my content? Can I request it be deleted as well? What if I'm suspended, rate-limited, or banned from posting questions or answers? What will happen to my votes? Will other users be impacted? Why wasn't my account deleted immediately after the timer expiring? What will happen to my pending bounties and close, reopen, delete, or undelete votes? I want my account deleted on all Stack Exchange sites. How do I do this? Will my profile on chat be removed once I delete my site account?   For more information, see &quot;&quot; in the .