Joining render layers
My objects are semi-transparent, and not one behind the other in the compositor
for working with MS word files in python, there is python win32 extensions, which can be used in windows. How do I do the same in linux? Is there any library? My cat sat on my laptop and now if I type either L or P, it inputs 3 or * instead. The rest of my keyboard still works correctly. The problem is bad enough that I had to use the touch screen of my computer to type this in.  How can I restore the correct working behaviour of my keyboard? Validity and Equivalence of two definitions of the real exponential function The Problem :  We state the following two definitions of the real exponential function from the . We're interested in showing that the two definitions are valid $($i.e. the defining sequence/series does converge to a unique real number$)$ and that the two definitions are equivalent.   I'm stuck at a couple of points $($which are described in highlighted lines$)$. Any help would be much appreciated. Thank you!     Definition $1$. The exponential function can be defined as the following limit of a sequence $$\exp x := \lim_{n \to \infty} \left({1 + \frac x n}\right)^n$$      Definition $2$. The exponential function can be defined as a  $$\exp x := \sum_{n = 0}^\infty \frac {x^n} {n!}$$   My Progress and two places where I'm stuck : Essentially the solution consists of three parts,  namely validity of definition $1$, validity of definition $2$ and equivalence of the two definitions.     Validity of Definition $1$. I'm stuck here! Can we show that the sequence $(a_n)$ given by $a_n = \left(1+\frac{x}{n}\right)^n$ converges for every $x \in \mathbb{R} ??$ Is it eventually monotone and bounded $??$   Validity of Definition $2$. The  of the power series is $$r=\lim_{n \to \infty}\left| \frac{\frac{1}{n!}}{\frac{1}{(n+1)!}} \right|=\lim_{n \to \infty}\left| \frac{(n+1)!}{n!} \right|=\lim_{n \to \infty}(n+1)=+\infty$$ Thus the infinite series in the right-hand side of Definition $2$ converges to a unique real number for all $x \in \mathbb{R}$. Hence the definition is well-defined.  Equivalence of Definition $1$ and Definition $2$.  There's this  of Definition $1$ $\implies$ Definition $2$ in the Pr$\infty$fWiki page, but it's kind of under construction and I'm not really convinced by it. So I decided to try to take my own shot at it.  For all $n \in \mathbb{N} \cup \{0\},$ let  $$T_n=\left(1+\frac{x}{n} \right)^n, ~S_n=\sum_{k=0}^n \frac{x^k}{k!}$$ We have to show that $\lim_{n \to \infty} T_n = \lim_{n \to \infty} S_n$  Now, \begin{align} T_n &amp;= \left(1+\frac{x}{n}\right)^n\\ &amp;= 1+n\cdot\frac{x}{n}+\frac{n(n-1)}{2!}\cdot\frac{x^2}{n^2}+\cdots +\frac{n(n-1)\cdots 1}{n!}\cdot\frac{x^n}{n^n}\\ &amp;= 1+x+\left(1-\frac{1}{n}\right)\cdot \frac{x^2}{2!}+\cdots +\left(1-\frac{1}{n}\right)\cdots \left(1-\frac{n-1}{n}\right)\cdot \frac{x^n}{n!} \end{align}  Clearly, $$S_n-T_n=\left\{1-\left(1-\frac{1}{n}\right)\right\}\frac{x^2}{2!}+\cdots +\left\{1-\left(1-\frac{1}{n}\right)\cdots \left(1-\frac{n-1}{n}\right)\right\}\cdot \frac{x^n}{n!}\geq 0$$     I'm stuck at this point. Can we show that $S_n-T_n \leq B_n$ such that $B_n \to 0$ as $n \to \infty ??$ Are there any free/open source alternatives to Adobe After Effects? I've been a illustrator and graphic designer for a number of years and now I'm looking to go more into motion graphics and visual effects. Is there anything that is open source/free (not a demo, education version or trial) that is as complex and feature-rich as Adobe After Effects but for Linux? I've tried Cinlerra, kdenlive, openshot and Blender and whilst they are good at video editing (and 3d modelling in Blender's case) they fall short in effects and compositing features.  I've also tried , but the project recently closed and the last update was quite buggy.  Also,  doesn't work and hasn't been updated in many many years, so don't mention it ;-) How prove $\frac{a^2}{a+2b^2}+\frac{b^2}{b+2c^2}+\frac{c^2}{c+2a^2}\ge 1$ let $a,b,c$ be postive real numbers ,and such $$ab+bc+ac=3$$   show that   $$\dfrac{a^2}{a+2b^2}+\dfrac{b^2}{b+2c^2}+\dfrac{c^2}{c+2a^2}\ge 1$$   This problem is from Secrets In Inequalities volume 1  page 30,example 1.24. the comment.the  author this case is a bit more diffcult,But this author can't post solution.Thank you Calculating path sinuosity in postgis is a fairly straightforward concept. How can this be calculated in postgis given a series of linestrings that represent the path? Every subsequence of $x_n$ has a further subsequence which converges to $x$. Then the sequence $x_n$ converges to $x$. Is the following true? Let $x_n$ be a sequence with the following property: Every subsequence of $x_n$ has a further subsequence which converges to $x$. Then the sequence $x_n$ converges to $x$.  I guess that it is true but I am not sure how to prove this. My question is similar to  except it's about VMware Workstation Player instead of VirtualBox.  How do I disable mouse integration? I want the VM to "capture" my mouse. One option is to pass my mouse directly to the VM, but that's more difficult if I need to exit the VM (I want to just use Ctrl+Alt).  I'm using "VMware Workstation 15 Player (Non-commercial use only)" VS Code Salesforce plugin deploy does not provide an error message VS Code plugin for salesforce seems to be broken yesterday, It does not provide proper error message in case of failure.  Tried this in a developer org as well as scratch org. Neither deploy code or push gives an error message, and every time we need to go to Salesforce setup -> Deployment Status to view the details.  Is anyone aware of any workaround? Java: Sorting user-input array upon return If I buy a game from PSN on ps3 Is it permanently mine? Using Inclusion/Exclusion to solve $x_1+x_2+x_3=15$ with $x_1,x_2\leq 5$ and $x_3\leq 7$ for non negative integers $x_1,x_2,x_3$ I want to solve for:     Number of integers solutions to the equation $x_1+x_2+x_3=15$ with $x_1,x_2\leq 5$ and $x_3\leq 7$ for non negative integers $x_1,x_2,x_3$   How can this be done using the principle of inclusion/exclusion? Should I use "got" or "gotten" in the following sentence? How do I get a tourist visa/card for Cuba? How do I get a tourist visa (or a tourist card) for Cuba?  I live in the Netherlands, but I'm not a Dutch citizen, I have an Italian passport. What is the Fastest a Character Can Move in One Turn? At level 20 with any magic items in the DMG, and any spells, what is the fastest a DnD 5e character could move using their movement?  (i.e., not including teleportation) If a black body is a perfect absorber, why does it emit anything? I'm trying to start understanding quantum mechanics, and the first thing I've come across that needs to be understood are black bodies. But I've hit a roadblock at the very first paragraphs. :( According to :     A black body (also, blackbody) is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence.   OK, that's nice. It's an object that absorbs (takes in itself and stores/annihilates forever) any electromagnetic radiation that happens to hit it. An object that always looks totally black, no matter under what light you view it. Good. But then it follows with:     A black body in thermal equilibrium (that is, at a constant temperature) emits electromagnetic radiation called black-body radiation.   Say what? Which part of "absorbs" does this go with? How can it absorb anything if it just spits it right back out, even if modified? That's not a black body, that's a pretty white body if you ask me. Or a colored one, depending on how it transforms the incoming waves.  What am I missing here? Use biblatex and utf8 For my thesis, I use biblatex for the bibliography.  As seen , biblatex is not compatible, with \usepackage[utf8x]{inputenc}. It was reported as close but I still have the same problem with my version of bibtex (last one on archlinux ). I want to use the € symbol inside my report but it fails without utf8.  ! Package biblatex Error: Incompatible package 'ucs'.  See the biblatex package documentation for explanation. Type  H &lt;return&gt;  for immediate help.  ...                                                l.7 \begin{document}   Any idea idea how to fix ?  \documentclass{report}  \usepackage[utf8x]{inputenc} \usepackage{biblatex} \bibliography{includes/mybib}{}  \begin{document}  X said Y \cite{bib1}  \printbibliography  \end{document}   and the file mybib  @online { bib1,        title = {Refrence title},        author = {X},        url = {http://site.com/y}} Drush 6 works great of corse on a Drupal 6 website, but will I have all of the Drush 6 features when working on a Drupal 7 website? Should I use Drush 7 when working on a drupal 7 website?  I found this post that says you can switch between the two version easily, is this correct?  switch to drush6 command: composer global require drush/drush:6.*  switch to drush7 command: composer global require drush/drush:dev-master The Windows 8 version of Google Chrome seems to have been updated to support the UI formerly known as Metro.  However, this seems to be the only option now, which means that I can no longer use Chrome on my netbook.  How do I get Google chrome to work in classic desktop mode on Windows 8?  Thanks How to give name to topics created using LDA?