Can't install/update/remove apps "trying to overwrite... which is also in..."
dpkg error: "trying to overwrite file, which is also in..."
Finding $\lim_{n\to\infty}\int_0^{\frac{1}{2^n}}(1+\cos(x))^n\,dx$ During our studies on Riemann Integrals we were given the following question in my Calculus II course: $$ \forall n\in\mathbb{N}: \text{let } f_n(x)=(1+\cos(x))^n, f_n:[0,1]\to \mathbb{R}$$ $$\text{ Find}: \lim_{n\to\infty}\int_0^{\frac{1}{2^n}}f_n(x)\, dx $$ I have tried finding the limit using the squeeze theorem. I noticed that the function is defined on $[0,1]$, where $\cos(x)$ is positive and decreasing. I used the following boundaries: $$ 1\leq f_n\leq 2^n \implies \frac{1}{2^n} = \int_0^{\frac{1}{2^n}}1 \leq \int_0^{\frac{1}{2^n}}f_n(x) \leq \int_0^{\frac{1}{2^n}}2^n = 1  $$ but $ \displaystyle{\lim_{n\to\infty}}\frac{1}{2^n} = 0 $ which means I'm unable to apply the squeeze theroem. I've tried using tighter lower boundaries such as $1+\cos(1)$ But it didn't seem to work. I did some trial and error by calculaing the integrals manually for different values of $n$ and it does seem like $\displaystyle{\lim_{n\to\infty}}\int_0^{\frac{1}{2^n}}f_n(x) dx = 1 $ This means that somehow I should find a lower bundary which tends to 1 when $n\to\infty$. Any ideas on how to go forward from here are welcome. In an ordered field we have $x^2 \ge 0$, hence the equation $-1 = x^2 + y^2$ has no solution. But what about finite fields in general? What is the solutions set $$  -1 = x^2 + y^2 $$ of this equation? This is the third time I've tried to install Ubuntu Server 14.04.03 64-bit on the same laptop, and each time it caused different problems.  Each time I wrote the same iso image to a USB flash drive by using a different application and OS.   Universal USB Installer (pendrivelinux.com) from Windows WinImage writer from Windows built-in image writer from Linux Mint 17.2    The iso image is the same in all three cases, the USB flash drive is the same, and the laptop is the same. However each time the installation of Ubuntu gave me different installation options. For example, the last time I installed Ubuntu, it didn't show all the packages to choose while installing (Basic Ubuntu server, etc.). Synthetic division of polynomials by factor of the form $(ax+b)$ By accident, I messed up a configuration file. How do I recover the default version without reinstalling or affecting other things? Troubleshooting "Windows cannot be installed to this disk. The selected disk has an MBR partition table" I recently bought a desktop computer with Windows 7 Home Premium x64 preloaded (OEM). I tried to install Windows 7 Ultimate x64 on this computer but I was presented with the following error message:     Windows cannot be installed to this disk. The selected disk has an MBR   partition table. On EFI systems, Windows can only be installed to GPT   disks.   The 1TB HDD on this computer has three partitions:   SYSTEM 100 NTFS - Healthy (System, Active Primary Partition)  OS (C:) 9148.04 GB NTFS - Healthy (Boot, Page File, Crash Dump, Primary Partition)  HP_RECOVERY (D:) 13.37 GB NTFS - Healthy (PrimarynPartition)   I'm trying to install a clean copy of Windows. I have a lidar file (file.las) with the following spatial reference:  Spatial Reference:            PROJCS["NAD83 / UTM zone 11N",     GEOGCS["NAD83",         DATUM["North_American_Datum_1983",             SPHEROID["GRS 1980",6378137,298.2572221010002,                 AUTHORITY["EPSG","7019"]],             AUTHORITY["EPSG","6269"]],         PRIMEM["Greenwich",0],         UNIT["degree",0.0174532925199433],         AUTHORITY["EPSG","4269"]],     PROJECTION["Transverse_Mercator"],     PARAMETER["latitude_of_origin",0],     PARAMETER["central_meridian",-117],     PARAMETER["scale_factor",0.9996],     PARAMETER["false_easting",500000],     PARAMETER["false_northing",0],     UNIT["metre",1,         AUTHORITY["EPSG","9001"]],     AUTHORITY["EPSG","26911"]]   Then I reproject it to WGS84 with las2las:  las2las --a_srs EPSG:26911 --t_srs EPSG:4326 -i file1.las -o output.las   And I get:   Spatial Reference:                GEOGCS["WGS 84",         DATUM["WGS_1984",             SPHEROID["WGS 84",6378137,298.257223563,                 AUTHORITY["EPSG","7030"]],             AUTHORITY["EPSG","6326"]],         PRIMEM["Greenwich",0],         UNIT["degree",0.0174532925199433],         AUTHORITY["EPSG","4326"]]   But when I try to revert the transformation: from WGS84 to NAD83/UTM 11N, I get an error:  las2las --a_srs EPSG:4326 --t_srs EPSG:26911 -i output.las -o wgs2utm.las ERROR 1: latitude or longitude exceeded limits error: Could not project point for ReprojectionTransform::latitude or longitude exceeded limits0.   Why I got this error, if I am just reversing the transformation (originally from NAD83 to WGS84, and then from WGS84 to NAD83)?. How do I install and use the latest version of GNOME? I followed the instructions for compiling GNOME Shell and it did compile with a few errors here and there but it didn't run. I installed GNOME Shell using sudo apt-get install gnome-shell but I got version 2.31.x, while the latest is 2.91.5 or something. So is there a way for me to install the latest build?   Is there some repository available for the latest build? Differential Geometry-Wedge product How can we prove the following relation for differentiating the wedge product of a p-form $\alpha_p$ and a q-form $\beta_q$$$d(\alpha_p\wedge\beta _q)=d\alpha_p\wedge\beta_q+(-1)^{p}\alpha_p\wedge d\beta_q$$ Proof of uniform limit of Continuous Functions The uniform limit of Continuous Functions is continuous.   Proof Let $\varepsilon &gt; 0$. There exists $N$ in natural numbers such that $n&gt;N$ implies  $|f_n(x)-f(x)| &lt; \frac{\varepsilon}{3}$ for all $x$ in $S$. In particular $|f_{N+1}(x)-f(x)| &lt; \frac{\varepsilon}{3}$ for all $x$ in $S$. Since $f_{N+1}$ is continuous at $x_0$ there is a $\delta&gt;0$ such that, $x$ in $S$ and $|x-x_0| &lt; \delta$ imply $|f_{N+1}(x)-f_{N+1}(x_0)|&lt; \frac{\varepsilon}{3}$ Now we conclude $x$ in $S$ and $|x-x_0| &lt; \delta$ imply $|f(x)-f(x_0)|&lt; 3 \cdot \frac{\varepsilon}{3} = \varepsilon$.  Can someone explain what is happening here? I don't follow it all. I'd like to determine the function corresponding to the following power series: $$x + \sum_{n=1}^\infty (-1)^n\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots2n} \frac{x^{2n+1}}{2n+1}, $$ where $|x|&lt;1$. What is the relationship between MIME types and File .extensions? I may have the wrong idea here, but I thought that:    MIME types are identifying codes, embedded inside a file. File .extensions are idenifying codes, suffixed to the file's name.   I thought, from something I heard in the dim dark ages, that Linux was .extension agnostic... ( maybe it was in the early days, and things have changed since then...? )  I've recently come from the Windows world, where, at the Operating-System level, a file .extension is the only way (as far as I know) to associate it with its relevant Application program.    Because I don't know why, I find it a bit disconcerting that a file named  "fred" and a file named "fred.txt" both open up in a Text Editor.    Is there a clear-cut hierarchy at work here? ERROR running force:source:pull: Entity of type 'CustomApplication' named 'Contact' cannot be found Transit Visa for Thailand Can I safely uninstall games purchased from Steam? Can I uninstall purchased games from my computer and then later download them through Steam without having to re-purchase if I'd like to?   I'm running short on space on my laptop, looking to free up some space and wanted to be sure that I can safely re-download anything at a later time similar to how you can with the Xbox Live marketplace. Which media player has seek preview with thumbnails? I was looking for a good video player to replace VLC, something that is as good as vlc but has seek preview. I am tired of fast forwarding in vlc  EDIT: I meant seek preview with thumbnails How do I reset an old iPod? My daughter gave her little brother her iPod Touch 8g. I have been trying to update the software and would like to get it rest to a factory clean state so I can linked it to the iTunes that already syncs to his iPad.   How can I do a clean up and wipe of everything from an iPod? Running programs in the background from terminal How do I run a program in the background of a shell, with the ability to close the shell while leaving the program running? Lets say my UI is having problems or for some reason, I need to boot up a program from the terminal window, say, nm-applet:  nm-applet   When it's started, it occupies the foreground of the terminal window.  Is there any simple way to run the program in the background without needing to leave the terminal open or have it occupy the whole terminal?  On that note, I did find a way to run programs from the terminal and have it allow for other inputs, by appending an ampersand (&amp;) to the command as such:  nm-applet &amp;   But this isn't much use as any processes started in the terminal are killed once the terminal is closed. Children’s books, one in space setting, the other in a jungle A hidden process, what it is? [root@datacenteronline ~]# ssh root@192.168.1.172 Last login: Wed Apr 17 09:55:45 2013 from 192.168.1.187 [root@localhost ~]# ls /proc/ | grep 2266 [root@localhost ~]# cd /proc/2266 [root@localhost 2266]# ls attr             cpuset   limits      net            root       statm autogroup        cwd      loginuid    numa_maps      sched      status auxv             environ  maps        oom_adj        schedstat  syscall cgroup           exe      mem         oom_score      sessionid  task clear_refs       fd       mountinfo   oom_score_adj  smaps      wchan cmdline          fdinfo   mounts      pagemap        stack coredump_filter  io       mountstats  personality    stat [root@localhost 2266]# ls -al /proc/2266 total 0 dr-xr-xr-x   7 apache apache 0 Apr 17 09:45 . dr-xr-xr-x 266 root   root   0 Apr 17 09:11 .. dr-xr-xr-x   2 apache apache 0 Apr 17 09:45 attr -rw-r--r--   1 root   root   0 Apr 17 09:45 autogroup -r--------   1 root   root   0 Apr 17 09:45 auxv -r--r--r--   1 root   root   0 Apr 17 09:45 cgroup --w-------   1 root   root   0 Apr 17 09:45 clear_refs -r--r--r--   1 root   root   0 Apr 17 09:45 cmdline -rw-r--r--   1 root   root   0 Apr 17 09:45 coredump_filter -r--r--r--   1 root   root   0 Apr 17 09:45 cpuset lrwxrwxrwx   1 root   root   0 Apr 17 09:45 cwd -&gt; / -r--------   1 root   root   0 Apr 17 09:45 environ lrwxrwxrwx   1 root   root   0 Apr 17 09:45 exe -&gt; /usr/local/apache2/bin/httpd dr-x------   2 root   root   0 Apr 17 09:45 fd dr-x------   2 root   root   0 Apr 17 09:45 fdinfo -r--------   1 root   root   0 Apr 17 09:45 io -rw-------   1 root   root   0 Apr 17 09:45 limits -rw-r--r--   1 root   root   0 Apr 17 09:45 loginuid -r--r--r--   1 root   root   0 Apr 17 09:45 maps -rw-------   1 root   root   0 Apr 17 09:45 mem -r--r--r--   1 root   root   0 Apr 17 09:45 mountinfo -r--r--r--   1 root   root   0 Apr 17 09:45 mounts -r--------   1 root   root   0 Apr 17 09:45 mountstats dr-xr-xr-x   6 apache apache 0 Apr 17 09:45 net -r--r--r--   1 root   root   0 Apr 17 09:45 numa_maps -rw-r--r--   1 root   root   0 Apr 17 09:45 oom_adj -r--r--r--   1 root   root   0 Apr 17 09:45 oom_score -rw-r--r--   1 root   root   0 Apr 17 09:45 oom_score_adj -r--r--r--   1 root   root   0 Apr 17 09:45 pagemap -r--r--r--   1 root   root   0 Apr 17 09:45 personality lrwxrwxrwx   1 root   root   0 Apr 17 09:45 root -&gt; / -rw-r--r--   1 root   root   0 Apr 17 09:45 sched -r--r--r--   1 root   root   0 Apr 17 09:45 schedstat -r--r--r--   1 root   root   0 Apr 17 09:45 sessionid -r--r--r--   1 root   root   0 Apr 17 09:45 smaps -r--r--r--   1 root   root   0 Apr 17 09:45 stack -r--r--r--   1 root   root   0 Apr 17 09:45 stat -r--r--r--   1 root   root   0 Apr 17 09:45 statm -r--r--r--   1 root   root   0 Apr 17 09:45 status -r--r--r--   1 root   root   0 Apr 17 09:45 syscall dr-xr-xr-x  29 apache apache 0 Apr 17 09:45 task -r--r--r--   1 root   root   0 Apr 17 09:45 wchan   Cound anyone tell me what it is?