Argue that the impromper integral $\int_1^\infty \frac{1-e^{-2x^2}}{x^2}$ for $x \neq 0$ is convergent
Argue that there exists a continuous function $g: \mathbb{R} \rightarrow \mathbb{R}$ which satisfies $g(x) = \frac{1-e^{-2x^2}}{x^2}$ for $x \neq 0$
How to recenter an object's origin? So, I'm working creating a lamp... yes, newbie here.  After modeling for a bit, I noticed that my point of origin was no longer the center of my object:    How to I reset an object origin point to the center of it's geometry? Does the alarm work when my phone is turned off? Variable variable class extensions in PHP--is it possible? Is something like the following possible in PHP?  $blah = 'foo1';  class foo2 extends $blah {     //... }  class foo1 {     //... }   This gives an error.  I want to dynamically set $blah so I can extend whatever class I want.  Edit: The reason for wanting to do this because I wanted to use a function out of another class in a related class. In the end it would have been something like:  Final extends foo1 extends foo2 extends foo3 extends foo4 extends parent { ... }   In the end I decided to instantiate the other class within the class and use it. Not the best options because they both you 2 of the same classes, but this won't be used that often, so it will work for now. How can I convert a vector to a cell array? Is WD-40 really bad to apply on bikes? I was told so but still see people doing that.   Also I saw WD-40 launching their new products of bike lubricant and degreaser. Did anybody try those? Word for low level noise among restless crowd, as sign of confusion or complaint? Dictionary gives me "drone" and "murmur" but I'm not sure if that's the word I am thinking of.  I want to use it to describe a group of people on strike who hear that their demands are not met and the CEO has resigned.  They're not shouting, but they're not whispering either.  They're restless and confused.  I want to say that a certain something (murmur?) was heard among the crowds, to indicate their state. Why rationalize the denominator? In grade school we learn to rationalize denominators of fractions when possible. We are taught that $\frac{\sqrt{2}}{2}$ is simpler than $\frac{1}{\sqrt{2}}$.  says that "there is a bias against roots in the denominator of a fraction". But such fractions are well-defined and I'm failing to see anything wrong with $\frac{1}{\sqrt{2}}$ - in fact, IMO it is simpler than $\frac{\sqrt{2}}{2}$ because 1 is simpler than 2 (or similarly, because the former can trivially be rewritten without a fraction).  So why does this bias against roots in the denominator exist and what is its justification? The only reason I can think of is that the bias is a relic of a time before the reals were understood well enough for mathematicians to be comfortable dividing by irrationals, but I have been unable to find a source to corroborate or contradict this guess. Why every map $f : S^n \to T^n (n>1)$ has topological degree zero? Why every map $f : S^n \to T^n (n&gt;1)$ has topological degree zero?  I don't know anything about covering spaces, and has been told to me that this assertion comes from this theory!  I do appreciate any help. I get different lightning render with the same scene camera setup.  Cycles render (both experimental and supported feature set) gets weaker lightning and needs more energy.  How can I get the same lightning and reflection setup with EEVEE and Cycles? A question about eigenvalues of $5\times5$ matrix Current  enables one to upgrade to macOS Mojave from a stable release, but I want to try out a fresh installation instead of upgrading with previous data, so that I can assess it better.  I've downloaded an application named "macOS Mojave Beta" from the App Store, and running it would presumably result in an upgrade. Now I wonder what to do next. Would  and booting from it be a good idea, when I'm working with a Beta version? It is stated that if $\psi(x_0)=\psi'(x_0)=0$ at some $x_0$, then $\psi(x)=0,\forall x$.  Hence, we cannot have the wavefunction and its derivative vanishing at the same point.  My question is, how to prove the above statement? What is Kirito's relationship with the girls of SAO? Ubuntu installation does not recognize drive partitioning I have a 1TB drive and installed Windows 7 on a 128GB partition.  When I now try to install Ubuntu 11.04 it does not recognize the Windows partition but offers the complete 1TB drive to install Ubuntu on instead. It displays:    However, in the Ubuntu Disk Utility the Windows partitions are recognized.    What do I need to do in order for Ubuntu to recognize the Windows 7 partition and install Ubuntu as a dual boot?   Response to comments  The following commands were executed and the results are shown below:  fdisk -l  WARNING: GPT (GUID Partition Table) detected on '/dev/sda'! The util fdisk  doesn't support GPT. Use GNU Parted.  Disk /dev/sda: 1000.2 GB, 1000204886016 bytes 255 heads, 63 sectors/track, 121601 cylinders Units = cylinders of 16065 * 512 = 8225280 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk identifier: 0x34a38165     Device Boot      Start         End      Blocks   Id  System /dev/sda1   *           1          13      102400    7  HPFS/NTFS Partition 1 does not end on cylinder boundary. /dev/sda2              13       16318   130969600    7  HPFS/NTFS  Disk /dev/sdb: 500.1 GB, 500107862016 bytes 255 heads, 63 sectors/track, 60801 cylinders Units = cylinders of 16065 * 512 = 8225280 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk identifier: 0x14a714a6     Device Boot      Start         End      Blocks   Id  System /dev/sdb1               1       60801   488384001   83  Linux   parted -l  Warning: Unable to open /dev/sr0 read-write (Read-only file system).  /dev/sr0 has been opened read-only. Error: /dev/sr0: unrecognised disk label How to get sitelinks to appear on Google Search? How to concatenate a variable number of csv, removing their header rows? after upgrading to 19.04 the Grub menu have become hidden. It still works and I can boot to both Windows 10 and Ubuntu by blindly finding the entry and pressing enter. I have tried to edit the /etc/default/grub and running sudo update-grub afterward but no change. Here is how it looks now:  # If you change this file, run 'update-grub' afterwards to update # /boot/grub/grub.cfg. # For full documentation of the options in this file, see: #   info -f grub -n 'Simple configuration'  GRUB_DEFAULT=0 GRUB_TIMEOUT=10 GRUB_DISTRIBUTOR=`lsb_release -i -s 2&gt; /dev/null || echo Debian` GRUB_CMDLINE_LINUX_DEFAULT="quiet splash" GRUB_CMDLINE_LINUX="" GRUB_TIMEOUT_STYLE=menu GRUB_HIDDEN_TIMEOUT_QUIET=false  # Uncomment to enable BadRAM filtering, modify to suit your needs # This works with Linux (no patch required) and with any kernel that obtains # the memory map information from GRUB (GNU Mach, kernel of FreeBSD ...) #GRUB_BADRAM="0x01234567,0xfefefefe,0x89abcdef,0xefefefef"  # Uncomment to disable graphical terminal (grub-pc only) #GRUB_TERMINAL=console  # The resolution used on graphical terminal # note that you can use only modes which your graphic card supports via VBE # you can see them in real GRUB with the command `vbeinfo' #GRUB_GFXMODE=640x480  # Uncomment if you don't want GRUB to pass "root=UUID=xxx" parameter to Linux #GRUB_DISABLE_LINUX_UUID=true  # Uncomment to disable generation of recovery mode menu entries #GRUB_DISABLE_RECOVERY="true"  # Uncomment to get a beep at grub start #GRUB_INIT_TUNE="480 440 1"   I can't use either Shift or Esc to make it visible too. After pressing either of these, Grub doesn't work anymore and I need to turn my laptop off and on in order to boot.  Edit: Not sure if it helps or not, but I just realized that if I go to the BIOS when I exit BIOS the grub menu shows up with no problem. The next time I boot, the grub menu is invisible again. Adding shapefile or feature class as layer in ArcGIS Desktop using Python/ArcPy? Stack Overflow is getting a Meta of its own Often I have a question, in a specific area (say Math SE or English SE) that is appropriate for the child meta of that site.   Then I realize it is not particular to the meta for that site but for Meta for all sites (like this question itself; I wanted a link to Meta Stack Exchange from meta.english, but realized no meta sites had such a link).  Wouldn't it be nice to have a link in all meta sites to Meta?