Let be $f$ a continuous function. Determine the limit $\lim\limits_{h \to 0} \frac{1}{h} \int_{a-h}^{a+h} f(x)\,dx$
Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be continuous.Let $t\in\mathbb{R}$. Evaluate:$\lim_{h\rightarrow0}\frac{1}{h}\int_{t-h}^{t+h}f(s)ds$
How to subtract a day from a date? Polynomial in $n$ variables it VS. this Vs. that Global inbox message not updated after comment edit At the moment, I have the latest notification in the global inbox, content of which does not correspond either to the comment itself or the copy of it on "recent responses" page. This seems like the comment was edited and the updated version was not copied to the global inbox.    ETA: OK, now this looks more coherent. Concatenating a string and primary key Id while inserting How would you show that if $ac≡bc$ $\mod m$ and $\gcd(c,m)=d$, then  $a≡b$ $\mod \frac{m}{d}$?  Any help would be much appreciated! Let $F : X → X$ be continuous. Prove that the set $\{x ∈ X : F(x) = x\}$ of fixed points of F is closed in X Here X is a Hausdorff Space.  I know that singleton sets, {x}, are closed in a Hausdorff space. Although Im not sure if thats how to use the Hausdorff property.   Should I investigate $h=F(x)-x$?  Can anyone give a hint lstlisting in two columns I would like to have two listings, side by side.  They have approximately the same length, therefore I don't care about how it's layed out if one part is longer.  I tried  \begin{minipage}{\textwidth} \begin{parcolumns}{2} \colchunk{\begin{lstlisting}[caption=code 1,frame=tlrb]{Name} void code() {  } \end{lstlisting}}  \colchunk{\begin{lstlisting}[caption=code 2,frame=tlrb]{Name} void code() {  } \end{lstlisting}}  \colplacechunks \end{parcolumns} \end{minipage}   while the border of the listings end up in chunks as follows:   Btw I'm using the texlive-package &amp; pdflatex on Ubuntu and the document class is  \documentclass[ a4paper, 10pt, twoside, openright, notitlepage, parskip=half, ]{scrreprt}   Any idea is appreciated. We have a view for a type of node that includes a Private File.  We cannot see a way to add an exposed filter, such as "Contains any word", and have it filter based on the file's name.  Are we missing something obvious? iMac with 8GB RAM -- memory always almost full Cannot start XAMPP on Ubuntu 11.10 I flagged a question, , as "low quality" but a moderator declined it. I thought that the post was a low quality one and would like to know why the moderator did not.  Hopefully shedding light on this matter will avail me of the knowledge to be a better flagger in future.  My logic was that mysql-fetch-row is not supposed to return an array of results. If it does than its name would be mysql-fetch-rows.  What's your take on the situation? A student prepares for an exam by studying a list of 12 problems. She can solve 9 of them. For the exam, the instructor selects 7 problems at random from the 12 on the list given to the students. What is the probability that the student can solve 5 of the 7 problems on the exam?  I am really confused by this problem. My first initial thought was to do:  (5 chose 7)(7 chose 0)/ (12 chose 7)  I am not 100% sure about this though. How is the ability of a person who gained physical access to your computer to get root with those steps in any way secure?   When grub2 menu opens press  e  to edit the Linux start options Change:   "linux   /vmlinuz-2.6.35-23-generic root=UUID=e7f1e48d-0015-485f-be7d-836217a31312 ro   quiet splash"    to:  "linux   /vmlinuz-2.6.35-23-generic root=UUID=e7f1e48d-0015-485f-be7d-836217a31312 ro init=/bin/bash"  Now you have root access just do:   mount -o remount,rw / passwd user mount -o remount,ro /  sync  reboot the computer and you win.   My question is, how is being able to break into any Linux machine through grub2 secure? I don't understand that fact about Linux, thank you for your answers. How do I logout from a non-registered account? I have a registered StackOverflow account which I normally log into using OpenID.  Recently I logged out in order to post a question anonymously (supplying a fake name and of my secondary email addresses).  The problem now is that I'm logged in to StackOverflow as this "dummy" user, unable to see a way to log out.  The top menu normally has a "logout" link, but when you aren't fully registered this link is replaced with "register".  There is no "logout" link for me. :(  So..   When logged out there is a "login" link. When logged in there is a "logout" link. When "logged in" with an unregistered account, there is only a "register" link (no "logout"). Drupal failed after update A sphere of radius R is rolling without slipping with a velocity v and collides inelastically with a step of height h &lt; R. What is the minimum velocity for which the sphere will be over the step?    Relevant equations  Total kinetic energy (maybe): $\frac{1}{2}I\omega^{2}+\frac{1}{2}mv^2$  Gravitational potential energy: $mgh$   Moment of inertia about a point a distance d from the CM from de center of mass: $I=I_{cm}+md^{2}$ Rolling without slliping  $v=\omega R$  A discussion of the problem This problem is confusing to me: I know the collision is inelastic so there is no conservation of kinetic energy, there is torque when the sphere pivots the step so the angular momentum is not conserved either, the linear momentum doesn't give a lot information and even though I tried to see what condition needs the torque about the pivot point (to give a net torque in the direction of rotation and thus passing the step), I'm not able to see which torque can overcome the one from gravity which doesn't let the sphere slide up:    The sphere has an angular velocity, but I'm missing something conceptual because I can't figure out how to formally state that the angular momentum changed the right amount so that the sphere made it past the step.  The attempt at a solution  My (almost certainly wrong) attempt was to say that the sphere lost kinetic energy because of the change on potential energy:  $\frac{1}{2}I\omega^{2}+\frac{1}{2}mv^2 +mgR = mg(R+h)\\ v=\sqrt{\frac{10}{7}gh} $  I hope you can help me :) Confusion in symbol of subset. If every element of set A ia an element of set B then we say that A is subset of B. A is said to be proper subset if A does not equal B.  My question is - whether the symbol we use to show subset is  same as that for proper subset? I have seen that A is subset of A itself is shown by the same symbol as that for the subset while when we write improper subset, we usually write equal to sign with symbol of subset. So, please help me to know this. I'm using Ubuntu 18.04.  I want to remove the digital clock from the lock screen because I just want to see a good wallpaper there, unobstructed.   How do I go about this? According to the official sources, is the radioactive green crystal that serves as Superman's Achilles' heel actually composed of the noble gas krypton, or is it supposed to be made out of some other substance? If so, what is that substance?