How to prove this criteria of differentiability?
Prove that $f$ is differentiable
How to find which RAM to get for my computer? I don't have any knowledge in hardware and would like to know which RAM should I buy for my laptop.  How do I discover what RAM I need &amp; how much my machine can take?  I have a Razer Blade 15 (RZ09-02705F76) 2018 but don't know if there is a specific type or format of RAM that suits it and don't know where to find this information. How to do this the fastest way? I recently watched  by Veritasium where he talks about the One Way Speed of Light and talks about the limiting case where in one direction the speed of light is $c/2$ while it's instantaneous in the other. He also says this is perfectly fine according to our Physics theories. He also points at Einstein's assumption in his famous 1905 paper where he assumes that the speed of light is same in all directions. This made me ask this question is taking the speed of light same in all directions an axiom of some sort? As I've often read no information can be sent at more than the speed of light but here one-way taking the speed to infinite makes no difference. So are all of our physics theories based on the assumption and what would happen if light turns out to be moving at different speeds in different direction? Will that enable transfer of information faster than the speed of light and is there any way for us knowing that the transfer happens faster than the speed of light? The video takes a Earth Mars case where he says it isn't possible for us to every realize this discrepancy but is there a more general proof which says it isn't possible Sharepoint Online/O365 custom fonts Partial adb restore ICS devices support creating backups using adb backup, and restoring them using adb restore. Using adb backup, one can select that everything should be backed up, or only a certain package.  However, adb restore lacks all the options of adb backup. When I call adb restore backup.ab, where backup.ab is only the backup of a single package, the phone shows me a warning dialog saying that all settings are going to be lost after restoring the backup. Is it true that restoring a single package backup wipes all data on the phone? If yes, is it somehow possible to restore a single package using adb restore? Please use UK pre-uni methods only (at least at first). Thank you. What is the best way to dump entire objects to a log in C#? i have a simple sort of a database file which consists only of entries in the following format     variable=value   i want to create a simple vim syntax highlighting for it and set it for specific file extension  for instance, variable part could be light blue, and value part light red  i googled it and came across things such as $vimruntime\syntax\, syntax set=, syntax match, and hi keywords, but couldn't set it up myself eventually  so i want a very simple vim code snippet that would realize it by matching the left and right hand sides and coloring them separately Let $n \geq 1$ be an odd integer. Show that $D_{2n}\cong \mathbb{Z}_2 \times D_n$. Let $n \geq 1$ be an odd integer. Show that $D_{2n}\cong \mathbb{Z}_2 \times D_n$. I define a map $$\phi:D_{2n} \rightarrow \mathbb{Z}_2 \times D_n$$ by $R \mapsto (0,r^{\frac{n+1}{2}})$ and $M \mapsto(1,m)$. Then I am stuck at showing the map is bijective. By the way, do we need to show that $(0,r^{\frac{n+1}{2}})(1,m)(0,r^{\frac{n+1}{2}})^{-1}=(1,m)$ ? If we can prove this, then what can we conclude? In Chamber of Secrets, in the first Duelling Club class, Snape suggests Malfoy use the Serpensortia spell against Harry. This of course reveals that Harry is a Parselmouth, but how could Snape anticipate this? Was there any reason for Snape to suspect Harry is a Parselmouth? Or was it just a way to laugh at how Harry would get frightened? Do local flows of left-invariant vector fields satisfy $\Phi_X^t\circ L_x=L_x\circ \Phi_X^t$? Given $G$ a lie group and $X$ a left-invariant vector field. Let $\Phi_X^t$ be the local flow of $X$. Why can we conclude that $\Phi_X^t \circ L_x=L_x \circ \Phi_X^t$? Thanks! Reducing resolution of huge categorical raster in QGIS? Run VirtualBox in background, without a window? msbuild, defining Conditional Compilation Symbols I'm possibly just blind, but is there a command line to specify conditional compilation symbols in MSBUILD?  I currently have this Line in my buildscript:  SET MSBUILD=C:\WINDOWS\Microsoft.NET\Framework\v2.0.50727\MSBuild.exe SET CONFIG=Debug %MSBUILD% /p:Configuration=%CONFIG% /p:OutputPath=..\..\output source\MyProject\MyProject.csproj   And I'd like to add a condition. In Visual Studio, i can just go into Project Properties => Build => Conditional compilation symbols, but I have not seen that option for msbuild?  Bonus Karma if you know if I can completely override all symbols already specified in the .csproj files to make sure that only the conditionals from my Buildscript go in. Random string that matches a regexp How do I fix "The expression of type List needs unchecked conversion...'? In the Java snippet:  SyndFeedInput fr = new SyndFeedInput(); SyndFeed sf = fr.build(new XmlReader(myInputStream)); List&lt;SyndEntry&gt; entries = sf.getEntries();   the last line generates the warning   "The expression of type List needs unchecked conversion to conform to List&lt;SyndEntry&gt;"  What's an appropriate way to fix this? food safety regarding re freezing twice cooked chicken Injectivity and surjectivity of a recursive function Let $f:\mathbb{N} \to \mathbb{Q}^+$ defined as follows : $$\begin{cases} f(0) = 0 \\ f(2n) = \dfrac{1}{f(n)+1} \\ f(2n+1) = f(n)+1 \end{cases}\,.$$ It is asked to prove the injectivity then the surjectivity of $f$.  After examining first values taken by $f$, I proved by induction that $f(2^k)=\dfrac{F_k}{F_{k+1}}$ where $(F_n)$ is the fibonacci sequence. Also one notes that if $m$ and $n$ have different parity then we can't have $f(m) = f(n)$ since $f(2\mathbb{N}) \subset (0,1)$ and $f(2\mathbb{N}+1) \subset [1,+\infty)$. Any ideas on how to finish the proof of injectivity and any thoughts about surjectivity are welcome. Thanks Text gets stretched or disappears when scrolling When scrolling in the Stack Exchange Android app, the text gets stretched vertically, code disappears, and sometimes the entire post content disappears.  This doesn't make the app completely useless, but it's pretty close.   Motorola Razr MAXX, Android 4.0.4. I'm having a heck of a time trying to disable the option  "Check for updates Automatically"  I ran composer to see what plist was being modified and it looks like ~/Library/Preferences/com.oracle.javadeployment.plist  &lt;?xml version="1.0" encoding="UTF-8"?&gt; &lt;!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN"    "http://www.apple.com/DTDs/PropertyList-1.0.dtd"&gt; &lt;plist version="1.0"&gt; &lt;dict&gt;     &lt;key&gt;/com/oracle/javadeployment/&lt;/key&gt;     &lt;dict&gt;         &lt;key&gt;deployment.macosx.check.update&lt;/key&gt;         &lt;string&gt;false&lt;/string&gt; &lt;/dict&gt; &lt;/dict&gt; &lt;/plist&gt;   So I experimented with changing that value to true or false and it would not effect the checkbox under the Java Control Panel > Update > Check for Updates Automatically  Your assistance would be much appreciated.  Initially I was looking @ /Library/Internet\ Plug-Ins/JavaAppletPlugin.plugin