How to install Ubuntu on a Chromebook 3?
True Ubuntu on Chromebook ARM
$\lim_{x \to 0} f(x)=\frac{\tan 3x}{\tan 2x}$ without L'Hospital How do I convert the coordinates of a click to a tilemap position? How do you turn a tilemap (produced by TileD) for cocos2d where I can click on individual items and get a callback?  Is it just a case of converting captured touch and finding out where it is on the tilemap and then converting that to pixels  -- but that doesn't say what item was clicked on.  I have a tilemap of a city with buildings on it, and I'd like to be able to click or press on a specific building, get a callback.  What would be the best way to accomplish this? Galactic Rotation Speeds - Ehrenfest Paradox, Gravitational time dilation, Dark Matter - all of the above? Combining two sorted lists in Python I have two lists of objects. Each list is already sorted by a property of the object that is of the datetime type. I would like to combine the two lists into one sorted list. Is the best way just to do a sort or is there a smarter way to do this in Python? Derivative (or differential) of symmetric square root of a matrix Let A be a square, symmetric, positive-definite matrix.  Let S be its symmetric square root found by a singular value decomposition.  Let vech() be the half-vectorization operator.  Is there a convenient expression for the derivative (or differential) of vech(S) with respect to vech(A)?  I know the expression for an inverse, which is sort of like a matrix version of the power rule.  Would this approach work for a symmetric square root as well (i.e., (1/2)S^(-1/2))? Use the triangle inequality to show that $|a|+|b| \leq |a+b|+|a-b|$ How would I go about proving that  $$|a|+|b| \leq |a+b|+|a-b|$$  Using the triangle inequality?  I tried squaring both sides, yielding:  $$|a|^2 +|b|^2 +2|a||b| \leq 2|a|^2+2|b|^2+2||a|^2-|b|^2|$$  Is it correct to move the terms to the other side? I tried $$2|a||b| \leq |a|^2+|b|^2+2||a|^2-|b|^2|$$ Then it is obvious that  $$0\leq |a|^2+|b|^2-2|a||b| +2||a|^2-|b|^2|$$ $$0\leq (|a|-|b|)^2 +2||a|^2-|b|^2|$$ $$0\leq ||a|-|b||^2 +2||a|^2-|b|^2|$$  But I have neither used the triangle inequality, nor it looks mathematically rigorous for my real analysis class. Any tips and tricks for solving these problems? How to run updmap-sys after installing cm-super? My original question was:   The answer that seems suitable to my cause is to install cm-super. I did that (using package manager [winxp 32 bit, MikTex installation 2.9 recently updated]). But still the command  \usepackage{cm-super}    yields an error.  User H Cavendish suggested to run updmap-sys, but I am not sure about how to do that on WinXP.   2011 November 04 edit: I made it sure that I have installed 'cm-super' - but still get the same error:   I have also tried updating the file name databases - but no avail. Effects:  +25 attack damage +15% life steal +40% attack speed Passive  Unique: Your attacks deal 5% of the target's current health in physical damage (60 max vs minions and monsters). Active   Unique: Drains target champion, dealing 15% of the champion's maximum Health in physical damage and healing you by the same amount. Additionally you steal 30% of their movement speed for 4 seconds - 60 second cooldown. (500 range)  Cost: 3200g VS.   Effects:  +70 attack damage +12% life steal Passive: Gain +1 attack damage and +0.2% life steal per kill (maximum +30 attack damage and +6% life steal). Half of the bonuses are lost upon death.  Cost: 3200g What is better for what situations, and when should you build BT instead of BotRK and Vice Versa. Which provides more lifesteal, the only variable being the stats of the weapon? I find myself constantly questioning my decision on which weapon to get and would really love some in depth answers. Would be great if any examples given were given from the ADC side of the house. I added a user account to the admin group and discovered I added wrong user. So I now have to remove the account from the admin group.   How can I remove an account from a group without deleting the user? Let $f:R\rightarrow R$ be a function such that all its successive derivatives exist in all $R$ and also $f(x)f''(x)\leq 0$ everywhere.  If $\alpha$ and $\beta$ be two successive roots of $f(x)=0$.   Then prove that $f'''(x)=0$ for atleast one $\gamma \in(\alpha,\beta)$.  My Attempt:  I began by taking an example $f(x)=(x-1)(2-x)$ and let $x=1$ and $x=2$ be its two successive roots.The statement is trivially true.  Then I took the function $f(x)=e^{-x}(x-1)(2-x)$.The statement is true here also so on and so forth.  But what would be the exact proof I wonder. It appears to be a question of Rolle's Theorem. Is it true that the order of $ab$ is always equal to the order of $ba$? I am Haitian, and traveling with a Haitian passport. I have to go to London with a work permit (tier 2 visa) on the 29th of July but I have 2 hour transit in Dublin.  Do I need a transit visa? Can I get it at the airport?  I also have a valid US visa. How to switch from Natbib to Biblatex in pre-made document class/template? I am using  to write my thesis. The template uses Natlib for references, whereas I really need Biblatex.   When I simply try to change \usepackage[natbib] for biblatex I get the error message  This is BibTeX, Version 0.99d (TeX Live 2016/Debian) Capacity: max_strings=100000, hash_size=100000, hash_prime=85009 The top-level auxiliary file: aagot-1-report.aux The style file: acm.bst Illegal, another \bibstyle command---line 80 of file aagot-1-report.aux  : \bibstyle  :          {acm}  I'm skipping whatever remains of this command Database file #1: Mendeleytry.bib.bib Warning--I didn't find a database entry for "" You've used 14 entries,code here   The solution  \usepackage[backend=bibtex, natbib=true, style=numeric]{biblatex}   didn't work.  Another possible solution was said to be to recompile from scratch to delete the .aux file, but that resulted in  /usr/share/texlive/texmf-dist/tex/latex/biblatex/biblatex.sty:462: LaTeX Error:  Command \bibhang already defined.            Or name \end... illegal, see p.192 of the manual.  See the LaTeX manual or LaTeX Companion for explanation. Type  H &lt;return&gt;  for immediate help.  ...                                                l.462 \newlength{\bibhang}   I have tried to use this "marco" to override the \requirePackage settings, but that also didn't work and resulted into  LaTeX Error: Two \documentclass or \documentstyle comm ands.  See the LaTeX manual or LaTeX Companion for explanation. Type  H &lt;return&gt;  for immediate help.  ...                                                l.45 \documentclass[whitelogo]{                            tudelft-report}    Where I can't seem to delete any of the document classes without getting the functionality of the tudelft-package and the biblatex citing (or in fact getting it to work at all!)  (no line number): [0] Config.pm:343&gt; INFO - This is Biber 2.5 [0] Config.pm:346&gt; INFO - Logfile is 'aagot-1-report.blg' [62] biber:290&gt; INFO - === Tue Apr 24, 2018, 22:24:06 [246] Utils.pm:165&gt; ERROR - aagot-1-report.bcf is malformed, last biblatex  run probably failed. Deleted aagot-1-report.bbl [246] Biber.pm:113&gt; INFO - ERRORS: 1   Is there any way I can still make this template work with Biblatex? Natlib seems to deeply rooted in the file and I don't know how to change it/access the settings/the ".sty"-file. Can I use the example documentclass combined with biblatex (instead of the standard natbib) without losing the great parts of the rest of the document class?  Thanks very much :) Change password on root user and user account How to switch 7 wires with a single on/off slide switch I am working on a project, where I want to build a raspberry pi into a nintendo 64 console, and be able to switch between with a single switch. By that I mean, I want to be able to use a single slide switch to either switch on the raspberry, or the n64.   I already figured the most stuff out, but I need help with wiring the controller port.   I have a n64 to USB controller adapter, which is connected to the raspberry. Each controller has 3 pins, VIN, GND and Data. I have 2 ports I need to switch. I also need to switch the usb Power for the raspberry.   So, I need a single switch, which has 2 states (ON, OFF), to switch the n64 controller ports to either the n64 console, or to my USB adapter. It also needs to switch the 2 wire power for the raspberry. I made some pictures to visualize it better:  So here is how it should be for to work with the regular N64. The controller ports are wired to the n64 console, and the raspberry power is not connected.    Then, when you switch it over to work with the raspberry, the n64 controller ports should go to the USB adapter, and the raspberry power is connected.    Now, my problem is I don't know how to achieve that. I know there are slide switches with enough pins, but they have multiple possibilities, not only two.   I also need something small, since the n64 case is small and doesn't have a lot of space.   Any ideas? VAR or VECM for a mix of stationary and nonstationary variables I have 4 time series. One of them is stationary and rest of them are not. I need to find relation between them. I will use AIC to decide lag length.   Should I use VAR or VECM to find relation between them?  Will VAR or VECM give me relation in terms of equation which can be used for forecasting?  Do I need to perform Johansen's test of cointegration?  What good would it do? How to delete (invalid) files with colon in their name under Windows? We have two sets: set No.1 and set No.2 as in this picture:   The observer is fixed to set No.1 . He sees set No.1 motionless and observes set No. 2 approaching with velocity 100,000 m/s.   Each set has one lamp and two, so called, touchers. Each set is designed so that if both touchers are touched simultaneously the lamp is turned on otherwise it remains off.  Set No. 2 is approaching set No. 1 so that each toucher in each set will be touched twice by the touchers of the other set.  The observer on set No. 1 observes the distance between touchers in each set 10 meters. He thinks the lamps on set No. 1 will be turned on because touchers in it will be touched simultaneously.  My question: Will the lamp on set No. 2 be turned on? How if an electrical current flowing from one toucher in a set to the other proves simultaneous touching? How can I use wget to get files recursively if the username contains an @? Firstly my main goal is to try and get FTP files recursively in Centos.  However the actual FTP login contains an @ which ruins the syntax.  Is there some way to place the username in "double quotes" or some such equivalent such that I can use @in the username? How to format a USB drive? Possible Duplicate:             How to format a pen drive in Ubuntu? I have this pen drive which I made bootable using some other system (OS). But I need to format it from my Ubuntu 12.04. Please guide me.