How to force correct answers for Integrals of Cos[mx]*Cos[nx]?
How to code around known MMa special-case failures?
I have a notebook with no Scroll Lock key (or any shortcut using the 'Fn' key).  Somehow Excel 2010 got the Scroll Lock on. I see it left down in the status bar and now I can't navigate through cells using the arrow keys, which is pretty annoying. It wasn't turned on some hours ago, so I think I must have hit some Scroll Lock toggle shortcut in Excel 2010 by mistake.  Anyone knows what hot to turn off Scroll Lock in Excel (shortcut or menu option)? Generalizing the case $p=2$ we would like to know if the statement below is true.  Let $p$ the smallest prime dividing the order of $G$. If $H$ is a subgroup of $G$ with index $p$ then $H$ is normal. Prove that if $(ab)^i = a^ib^i \forall a,b\in G$ for three consecutive integers $i$ then G is abelian Eclipse was working as good as anything on 14.04. I did a clean install of 16.04 and installed Eclipse. But it runs a Java program only once after which it just hangs during subsequent attempts before I remove and reinstall it. I have tried many things, since in the beginning I needed CDT as well. Right now, I just want to remove everything related to eclipse and do a fresh install (remove all the configs and dependencies). Please note that I used Eclipse installer to install Eclipse and the eclipse icon image is also not appearing (the default ubuntu ? is appearing). Can prematurely powering down a computer cause bad sectors in a hard drive? Proof that Limit of the Log is the Log of the Limit Proof that Limit of the Log is the Log of the Limit. What is the intuition behind this statement? How to mathematically evaluate a string like "2-1" to produce "1"? WINDOWS 10 - Error Windows Update 10 = Error in phase " SAFE_OS " with the operator error with " BOOT " For days I tried several ways to install Windows 10 . With Windows Update I have always an error and with the media creation tool microsoft I have this message: " The installation failed in SAFE_OS phase with an error when BOOT operator " with this code : 0xC1900101 - 0x20017 Having tried everything I do not know what to do ... Can you help me please ? Thank you  PS: I migrated my OS with the software "Paragon migrate OS to SSD" from my hard disk to my SSD. Maybe I have this errors because I did this.... I have a chromebook series 5. I want to install Ubuntu onto a USB stick. When I downloaded Ubuntu onto my USB stick, it won't start up.  Do I first have to download Ubuntu onto my chromebook hard drive, open Ubuntu and then make USB stick bootable? And then return back to chrome?  Or is there a way to download directly onto USB and make the stick bootable?  I appreciate any help. Anyone know a way to immediately show the seconds of a file's date modified property in the GUI? So if you create a file, any file in any directory, right-click and choose Properties, the date modified (if it's recent) will say something like "dd/mm/yyy hh:mm, one minute ago" - reminder this is in Windows 7. Windows XP did it normally. Then they changed something.  If you wait a while, eventually you'll see the seconds, I'm not sure how long a while is, but this is incredibly annoying if you want to troubleshoot something that relies on the seconds of timestamps... is there a setting? registry key I can change perhaps?  I'm literally using Chrome, pasting in the path of the directory to be able to see the seconds quickly (as a workaround) but would be nice to be able to use Win7. Show f is continuous on (0, ∞) iff f is continuous at 1 for a defined function. exercise: Suppose that $f:(0,∞) → R$  satisfies $f(x) - f(y) = f(x/y)$  for all $x,y$ in $(0, ∞)$ and $f(1) = 0$.   Prove f is continuous on $(0, ∞)$ if and only if f is continuous at $1$.    (proof→:) Suppose that $f:(0,∞) → R$ satisfies $f(x) - f(y) = f(x/y)$ for all $x,y$ in $(0, ∞)$ and $f(1) = 0$. Suppose f is continuous on (0,∞), then by definition f is said to be continuous at a point $a$ if for every $ε &gt; 0$  there is a $δ &gt; 0$ such that $|x-a| &lt; δ$ implies $|f(x) - f(a)| &lt; ε$.   Then suppose f is continuous at $1$, then by our defined function  f(x) - f(y) = f(x/y) , we get $|x-1| &lt; δ$ implies $|f(x) - f(1)| = |f(x) - 0| = |f(x)| =  &lt; ε$.   (proof ←) :Suppose that $f$ is continuous at $1$, then we need to show $f$ is continuous on every point $a$ on $(0, ∞)$. Thus, by definition, f is said to be continuous at a point $a$ if for every $ε &gt; 0$ there is a $δ &gt; 0$ such that $|x-a| &lt; δ$ implies $|f(x) - f(a)| &lt; ε$. Thus, $|x-a| &lt; δ → |f(x) - f(a)| = |f(x/a)| &lt; ε$. Then $f$ is continuous on on $(0, ∞)$.  Please can anyone please help me verify this makes sense. If not, can someone please give any feedback/hints. Thank you in advance. n-dimensional vector space isomorphic to the n-th product of a field as abelian groups Let $V$ be a finite dimensional vector space (of dimension n) over a field $F$. I need to show that $V$ is isomorphic to $F^n$ as abelian groups. However, I don't really understand what does "isomorphic as abelian groups" mean, my (poor) attempt to solve this was:  Let $f:V\to F^n$, $f((v_1,v_2,\ldots,v_n)):=v_1+\ldots+v_n$, clearly $f$ is a group homomorphism, but it is not biyective since, for example, in the case where $dim(V)=2$ and $F=\mathbb{R}$ we have $f((2,-2))=0=f((3,-3))$, I've also tried it by defining $f$ to be the product of a vector's entries but obviously it didn't work so I'm stuck!   I think this should be an easy problem but since I don't quite understand it, it's giving me problems. Thank you for your help. How to count the node a user has created in a View? Is $\{\emptyset\}$ a subset of $\{\{\emptyset\}\}$? $\{\emptyset\}$ is a set containing the empty set. Is $\{\emptyset\}$ a subset of $\{\{\emptyset\}\}$?  My hypothesis is yes by looking at the form of "the superset $\{\{\emptyset\}\}$" which contains "the subset $\{\emptyset\}$". My competitor is using Alexa to see what I am doing. I need to get stop Alexa from including my sites in their rankings. How can I do so?   Is it possible to deny access to any visitor with the Alexa toolbar and deny access to Alexa bot requests? Large text files load not working on android Suppose I installed ubuntu with the user usr1 then I added usr2. I then create a group grp1 where this 2 users are added. A folder is owned by usr1 and has group grp1. But when I login as usr2 I cannot write. The folder has permissions 755...  usr2@kmserver:/media/data/www$ groups usr1 usr1 : grp1 ... usr2@kmserver:/media/data/www$ groups usr2 usr2 : grp1 ... usr2@kmserver:/media/data$ ls -l total 20 drwx------ 2 root root 16384 2011-05-12 10:53 lost+found drwxrwxr-x 2 grp1   grp1    4096 2011-05-12 15:15 www   Whats wrong? I use a lot of lists and arrays but I have yet to come across a scenario in which the array list couldn't be used just as easily as, if not easier than, the linked list.  I was hoping someone could give me some examples of when the linked list is notably better. Use worksheet name as a variable in a lookup A half covered lens Let's say there's an object in front of a convex lens. I have a piece of paper behind the lens at the right location such that it will the lens will form an image on the paper. The object is illuminating.  Now if I put another piece of paper right before the lens, and cover up half of the lens. The image, instead of only half being visible, it will actually remain the same. The only difference is that it will be dimmer.  Now, the question is what if I remove the paper at the location where the image forms, and put my eye there. What will I see? Will I see the piece of paper which is blocking half of the lens at all? Does that mean I will just "see through" the paper?  I wanted to try this out myself, but unfortunately I don't have a lens besides me.