TikZ arrows.meta not usable in multiple pictures?
Is it possible to load a TikZ library locally?
Show that $\lim\limits_{a \to 0^+} \int^1_0 ax^{a−1}f(x)dx=f(0)$. Suppose $f$ is Riemann integrable on $[0,1]$ and continuous at 0. Show that $$\lim\limits_{a \to 0^+} \int^1_0 ax^{a−1}f(x)dx=f(0).$$   Can anyone share some insight on this one? I have no idea where to begin. Maybe a substitution? I have just upgraded to Ubuntu 17.10 and found out there is no option to have 2 by 2 workspaces. I was able to configure 4 "static" workspaces using , but I would like to have them in 2 rows by 2. Any ideas? Automatic pyqgis categorized renderer classification I have some layers in my project and I would like to alter their styles, since ranges of values for underlying columns have changed.  Normally it would require to enter each layer style settings separately and trigger "Remove All", and "Classify" button, however I would like to execute it from the code.   I found such method for graduated symbol:  renderer.updateClasses(layer,0,bins)   ,however I'm having trouble to find corresponding method for categorized symbol class  Is there any way to do this from pyqgis without the need to specify the layer style from the scratch (create category, label etc.) ? Some equivalent of "Classify" button from below screenshot: Selenium/PhantomJS raises error What is the minimum $ \sigma$-algebra that contains open intervals with rational endpoints What are the minimum $\sigma$-ring and $\sigma$-algebra on $\mathbb R$ which contain the open intervals with rational endpoints?  Is there a relation between this $\sigma$-algebra and Borels? Why aren’t my villagers breeding? I’ve got one villager up 7 blocks surrounded with 6 doors. On ground level I have villagers who are supposed to breed. They are willing, their inventories are full of potatoes, and I’ve been sitting here for hours.  Hearts are popping up above their heads but nothing happens. I am playing on Xbox One. It is will known that increasing cooling of a metal casting will lead to finer micro-structure which mean higher mechanical properties. If I have 2 molds one is thick copper die ,&amp; second is just thin-walled copper cup or mold cooled by water. which one of them excepted to cool the molten metal i.e. aluminium faster ?   by calculation it seems that copper die have higher cooling power as it has higher thermal diffusivity , but in real life it seems water have more cooling power. I am so confused. My multiple regression analysis model has a statistically significant F value however all beta values are statistically non-significant.   All the regression assumptions are met. No multicollinearity was found. Correlations among all predictors are all less than 0.60.   What else might be the cause of the insignificant predictors? Last time I asked a similar question but that was about svn related versioning info. Now I am wondering how to query windows "File version" attribute about eg. a dll. I payed attention to wmi and win32file modules as well without success. My refrigerator line is 20 amp with 12 gauge wire. Can I tap into that with 14/2 wire, and run a light switch and 1 LED light? Today I was told a tale by a Unix trainer where the root password got leaked to the students, and one of the fellas removed the execute permission from /usr/bin/chmod itself. How do you recover chmod in this case and make it executable again? Let's say getting it from an external source or recompiling it is not a preferable option, is there some smart hack that can recover this chmod itself?   Note that this happened a long time ago and I'm not looking for a solution for some current problem, just curious about what ways Unix provides us around such an issue. Make CMD-Delete a keyboard shortcut in Apple Mail to move a message to the archive? I start with knowing that two numbers are coprime if:  $n*k + m*j = 1$  So, setting $k = a$ and j = $a+1$ I can solve as follows:  $n*a + m*a + a$  Then,  $a(n+m) + m = 1$  Where can I go from here? Property of $\{0^n, 1^n, \ldots\}$ The differences between adjacent squares are the odd numbers:  0 1 4 9 16 25 …  1 3 5 7  9 …  The differences between adjacent odd numbers are 2 = 2!  I found that this truth is more general: If the differences between adjacent powers of $n$ are written out, and the differences of those differences etc, the $(n+1)$th sequence is {n!, n!, …}  Is this a well-known theorem? Does it have an easy proof? The app forgets that I voted when I scroll the question Related:   I am using 1.0.71 on KitKat.  Immediately after voting, the arrow is displayed in red and the vote count is correct. However, when I scroll to read answers and then back to the top, the arrow is grey again and the vote count is reset to the previous value.  A reload of the question (pulling the finger down) is needed to show the correct situation, which is kept from then on.  This case was on security.stackexchange.com but I observed the same behavior on other sites too.  Screenshots   original state:  upvoted:  scrolled down and back up  after a reload How to sort this JSON Given sequence of $L-$Lipschitz functions which converges pointwise, prove uniform convergence Let $f_n:[a.b]\rightarrow \mathbb{R}$ be sequence of $L-$Lipschitz functions, that is: $$\forall x,y\in[a,b]: |f_n(x)-f_n(y)|\leq L|x-y|$$   Suppose $f_n \rightarrow f$ pointwise, prove $f_n \rightrightarrows f$   I have all the parts of the puzzle for the proof, and I'm trying to put them all together, I'm using  in my answer.  I would appreciate is you could correct my proof, and if you have an alternative proof, I would be more then happy to see it.  My proof:   Let $\epsilon&gt;0.$  $f_n$ are uniformly continuous on $[a,b]:$  $\tag{1} \exists \delta&gt;0\ \forall x,y\in[a,b]: |f_n(x)-f_n(y)|&lt;\frac{\epsilon}{3}$  $f$ is also $L-$Lipschitz:  $\tag{2} \forall x,y\in[a,b]:|f(x)-f(y)|&lt;L|x-y|=\frac{\epsilon}{3}$  Let us set a partition of $[a,b]$ such as Stephen Montgomery-Smith suggests:     Pick points $x_1,\dots,x_m \in [a,b]$ which are distance   $\frac{\epsilon}{3}$ from each other.        For each $1 \le i \le m$, find a number $N_i$ so that for all $n \ge  N_i$ we have $|f_n(x_i)-f(x_i)| \le \epsilon/3$.   Let $N = \max_{1 \le i \le m} N_i$      Now given any $x \in [a,b]$, pick $1 \le i \le m$ such that $|x-x_i| &lt;\frac{\epsilon}{3L}:  |f_n(x)-f(x)|&lt;\frac{\epsilon}{3} \tag{3}$   $$\begin{align}|f_n(y)-f(y)| &amp;=|f_n(y)-f_n(x)+f_n(x)-f(x)+f(x)-f(y)| \\ &amp;\leq |f_n(y)-f_n(x)| + |f_n(x)-f(x)|+|f(x)-f(y)| \\ &amp;&lt; \frac{\epsilon}{3} + \frac{\epsilon}{3} + \frac{\epsilon}{3} = \epsilon \\\end{align}$$ regular expressions / pattern matching on ubuntu command line For some of the apps I've developed (then proceeded to forget about), I've been writing plain SQL, primarily for MySQL.  Though I have used ORMs in python like , I didn't stick with them for long.  Usually it was either the documentation or complexity (from my point of view) holding me back.  I see it like this: use an ORM for portability, plain SQL if it's just going to be using one type of database. I'm really looking for advice on when to use an ORM or SQL when developing an app that needs database support.  Thinking about it, it would be far better to just use a lightweight wrapper to handle database inconsistencies vs. using an ORM. Suppose that $U_n=\frac{1}{\sqrt{2n\sigma^2}}\left(\Sigma X_j-\Sigma Y_j\right)$,  where $X_1,X_2,\ldots$ and $Y_i,Y_2, \ldots$ are i.i.d. sequences of random variables with mean $\mu$ and variance $\sigma^2$ and the sequences $\{X_i\}$ and $\{Y_i\}$ are independent.  Then, for all real numbers $x$, show that, as $n\to \infty$,  $$\mathbb{P}(U_n\leq x) \to  \int_{-\infty}^{x} \frac{1}{(\sqrt(2\pi))} \:e^{-\frac 12{u^2}}\mathrm du $$ Approach  I tried to carry out the integration on the right, but this does not integrate nicely. It ends up involving an error function, so I figured this was the wrong was to go.  Should I be looking at convergence in probability to answer this question? Is Chebyshev's inequality relevant here? If so, how and how does that relate to the integral?