How to solve $\lim_{x\to\infty}\frac{x+\sin x}{x-\sin x}$ using L'Hopital rule
Problem applying L'Hopitals rule.
Black screen on boot after AMDGPU-Pro install (16.04) I have been having some screen freezing issues on my new Ubuntu 16.04 system, and have been in the troubleshooting process for this issue. I thought it was a graphics driver problem, as I am running an AMD R9 380x card which was supposed to be fully supported by the open-source AMDGPU driver preinstalled with 16.04, but after looking around online, many people seem to have issues with. I thought the answer would be to install the recently released AMDGPU-Pro driver , following the instructions from . However, when I reboot I am getting a black screen. Is there an easy way to revert my changes back? My machine was semi-functional with the freezing issue but now with no video at all is useless to me. How to proceed? $E[e_te_s\Delta B_t\Delta B_s]$ for $\Delta B_t$ Brownian motion increments and $e_t(\omega)$ a measurable function. For which values does the Matrix system have a unique solution, infinitely many solutions and no solution? Given the system:  $$\begin{align}  &amp; x+3y-3z=4 \\   &amp; y+2z=a \\  &amp; 2x+5y+(a^2-9)z=9 \end{align}$$  For which values of a (if any) does the system have a unique solution, infinitely many solutions, and no solution?    So I am getting that it has: infinitely many solutions at: (-1)    No solution at (1)    Unique solution at (-1,1)    AM I RIGHT?? Is this defined by the language? Is there a defined maximum? Is it different in different browsers? I'm looking for a word that describes a person who is extremely dismissive and unopen to ideas or comments. Dismissive  feeling or showing that something is unworthy of consideration   For example,  Tom: 'Get your table organised! It's so-' Jack: 'Shush, bring your comments somewhere else.' Artinian affine $K$-algebra Importing QGIS3 processing tools in standalone script Inspired by , but for QGIS 3 (and therefore Python 3), I would like to use the QGIS processing algorithms in a standalone Python script without a GUI, with a standard installation of Ubuntu Linux. A simple import processing is insufficient: import processing processing.run(    &quot;qgis:rasterlayerstatistics&quot;,    {        'INPUT': .'/somefile.tif',        'BAND': 1,        'OUTPUT_HTML_FILE': './result.html'    } )  Results in: Traceback (most recent call last):   File &quot;&lt;stdin&gt;&quot;, line 1, in &lt;module&gt; ModuleNotFoundError: No module named 'processing'  How do you get access to the QGIS processing module to use the QGIS processing algorithms in a standalone Python script (not the QGIS interpreter)? Where do I find system sounds? After installing gm-notify I see the option of hearing a sound every time a new e-mail arrives in my Gmail inbox, but I don't know where Ubuntu (10.4) stores the system sounds to assign one. Any ideas? Thanks. Regulated AC power supply? In C, what is the difference between using ++i and i++, and which should be used in the incrementation block of a for loop? I have seen in American Sniper, Dead-7 and Carrie that when someone is killed, they are laying on the ground with blood leaking out of their back or somewhere else on the body.  The puddle continuously grows with few signs of slowing down. This is obviously not CGI because it is a real liquid (may not be real blood as that would spark an emergency in real life).   I have seen in American Sniper that when the protagonist kills yet another enemy, they are filmed hitting the ground and blood starts pooling around their body.  In Carrie: In the dance room where Carrie sets her powers loose and kills a lot of teenagers in the process, there are a few that hit the ground with blood pooling under their bodies. Sometimes they would be on their side with blood coming out.  In Dead 7: Kimono and the other six killed lots of zombies. Some of the six were killed in the process as well before they came to Apocalypta to kill her. They were filmed hitting the ground dead with blood pooling around them.  I am not sure how they film this as they are wearing thin shirts for these scenes, and not only that, but the characters also have blood (obviously fake) only just dripping out of the side of their mouths (an indicator they have a ruptured and wounded stomach or lung (in this case the blood would be pink and frothy).  What is the film technique that allows this to happen? How to print every Nth character of a string? This line of code does exactly this except I want it to start at the first character not the 7th. $ echo 1234567890abcdefghijklmnopqrstuvwxy | sed 's/.\{1,7\}\(.\{0,1\}\)/\1/g'  What I'm looking for is 19gow how to disconnect main service drop at service panel 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. It seems that $\{e\}, \{e,s\}, \{e,rs\}, \{e,r^2s\},...,\{e,r^{n-1}s\}, \{e,r,r^2,...,r^{n-1}\}, D_n$ are always subgroups of $D_n$. Especially when $n$ is odd, these seem to be the only subgroups. But when n is even, say $n=4$, then there are also $\{e,s,r^2,r^2s\}$ and $\{e,rs,r^2,r^3s\}$. It makes me wonder, is there a general formula/algorithm for finding all subgroups of $D_n$ when $n$ is even? What is the difference between "What are you?" and "Who are you?"? I am often asked "Who are you?" and "What are you?", but I don't know the difference between these two questions.  Please explain it to me. Uniform convergence for sequences of functions A man enters a comatose author's dreams to wake him up This is a short story, I think, but I might be wrong.  A man is recruited to enter an authors' dreams to try &amp; bring him out of a coma &amp; finds himself in a hackneyed barsoom type world where the coma victim is a muscle bound hero, it's a desert world with two suns, the damsel in distress is the typical scantily clad princess trope.  The "hero" basically spoils the authors' dreams by manifesting a pistol &amp; simply shooting the monsters dead at one point &amp; the author tries to write him out of the "story" by simply jumping forward several chapters &amp; is both surprised &amp; peeved to find him still there.  The author eventually comes out of his coma &amp; immediately assaults the man when he recognizes him from his dreams, he tries to strangle him if I remember right.  He enters the authors' dreams with some kind of experimental dream imaging tech, basically a two ECG sort of set up linked through a computer with him put to sleep with drugs I think. Proof for maximal ideals in $\mathbb{Z}[x]$ I have been trying to prove the following theorem:      Every maximal ideal in $\mathbb{Z}[x]$ has the form $(p, f(x))$ where $p$ is prime integer and $f$ is primitive integer polynomial that is irreducible modulo $p$.    Idea: I tried to establish a homomorphism $\phi: \mathbb{Z}[x] \rightarrow \mathbb{F}$. Since $\mathbb{F}$ is a field it has characteristic $p$ and so integer prime p are mapped to 0 in $\mathbb{F}$. Hence $p\in \ker \phi$. Next we consider $\phi': \mathbb{Z}[x] \rightarrow \mathbb{Z_p}[x]$ and pick an arbitrary maximal ideal $M\in \mathbb{Z}[x]$. So, $\phi'(M)$ is maximal as long as $p \in M$ by correspondence. But now I am stuck at this stage and do not know how to proceed. I guess we might have to use primitivity given in problem but dont know how. postfix discard or change Message-ID header based on another header line I want to change the Message-ID header or better yet, discard it. I know everyone is going to ask "Why would you want to do that?" because I know it sounds weird to even write it.  Well I am developing a system that saves an incoming e-mail in EML format, changes it and sends it to the user, at some point the user can request to have the original EML sent to him/her. The issue is that when I re-send the EML it has the same Message-ID header which causes exchange servers to drop the re-send.  Of course I am hoping there is some option through postfix to do this, otherwise I will need to parse and change the EML but I rather not do that.  I tried to do this with "header_checks" and it works BUT I need to be able to do this conditionally, meaning only on a specific occasion, which I can identify by looking at the other headers, I want to remove the Message-ID. Subclassing tuple with multiple __init__ arguments