How to reconstruct a number from its integral, fractional and exponent parts?
How to manually parse a floating point number from a string
In my assignment I have to prove that the following function doesn't have a limit:  $$f(x)=\frac{x}{x-\lfloor{\sin x}\rfloor}$$ when $${x \to 0}$$  In other words, I have to prove that for every $\delta$ such that $0&lt;|x-{x_0}|&lt;\delta,$ $|f(x)-L|&gt;\epsilon$.  In fact, I don't even know how to start. Do I choose my $\delta$? I know that the sin function has certain values that's supposed to help me. How do I use it?  I have to prove this by definition, so I can't use limit arithmetic for example  Thanks. back-up: which patitions to back-up before upgrading/reinstalling I have Ubuntu13.04 on my laptop. I have to upgrade it to the next release or else I would install a fresh release after deleting my current system.  I have already installed and configured my current system a lot and I can't take the burden of doing it all over again if I install the next release. Now I would like to know that what all back-ups are required to be taken beforehand so that I would recover all my files/installations/configurations etc. In other words I should have everything on my new system (simply by restoring from back-ups) that I possess currently.  My current system has /, /boot, /home &amp; swap partitions which were created by me when I had freshly installed the O.S. Difference between == and === in JavaScript In which cases is a comma/period placed inside or outside of parentheses? Are there cases where a period is placed inside parentheses? In which cases the period (or a comma) should be placed inside the parentheses? When I check for updates, I get a "Failed To Download Repository Information" error.   This is what comes up under details:   W: Failed to fetch gzip:/var/lib/apt/lists/partial/us.archive.ubuntu.com_ubuntu_dists_natty_main_source_Sources  Hash Sum mismatch,  E: Some index files failed to download. They have been ignored, or old ones used instead. What is the relation between linear purity and von Neumann entropy of a state? Given a density matrix $\rho$, its linear purity is $\mathrm{Tr} \rho^2$, its von Neumann entropy is $-\mathrm{Tr} \rho \log \rho$. Knowing one how do I calculate the other?  Edit:   My thought is that the linear purity and the von Neumann entropy are a parallel set of benchmarks for mixedness. Their inter-conversion should be like unit conversion.  See it this way, as a state goes from a pure state to a maximally mixed state, $\mathrm{Tr} \rho^2$ goes from $1$ to $0$, and $-\mathrm{Tr} \rho \log \rho$ goes from $0$ to $\log d$, like two rulers. A point on one should correspond to a point on the other. I have a multiboot system set up. The system has three drives. Multiboot is configured with Windows XP, Windows 7, and Ubuntu - all on the first drive. I had a lot of unpartitioned space left on the drive and was reserving it for adding other OSes and for storing files there in the future.  One day I went ahead and downloaded Partition Wizard and created a logical NTFS partition from within Windows 7, still some unpartitioned space left over. Everything worked fine, until I rebooted the computer a few days later.  Now I'm getting:    error: unknown filesystem.   grub rescue&gt;   First of all I was surprised not to find any kind of help command, by trying:    help, ?, man, --help, -h, bash, cmd, etc.  Now I'm stuck with non-bootable system. I have started researching the issue and finding that people usually recommend to boot to a Live CD and fix the issue from there. Is there a way to fix this issue from within grub rescue without the need for Live CD?  UPDATE  By following the steps from , I was able to boot to initramfs prompt. But not anywhere further than that.  So far from reading the manual on , I was able to see my drives and partitions using ls command. For the first hard drive I see the following: (hd0) (hd0,msdos6) (hd0,msdos5) (hd0,msdos2) (hd0,msdos1)  I now know that (hd0,msdos6) contains Linux on it, since ls (hd0,msdos6)/ lists directories. Others will give "error: unknown filesystem."  UPDATE 2  After the following commands I am now getting to the boot menu and can boot into Windows 7 and Ubuntu, but upon reboot I have to repeat these steps.    ls ls (hd0,msdos6)/ set root=(hd0,msdos6) ls / set prefix=(hd0,msdos6)/boot/grub insmod /boot/grub/linux.mod normal   UPDATE 3  Thanks Shashank Singh, with your instructions I have simplified my steps to the following. I have learned from you that I can replace msdos6 with just a 6 and that I can just do insmod normal instead of insmod /boot/grub/linux.mod. Now I just need to figure out how to save this settings from within grub itself, without booting into any OS.  set root=(hd0,6) set prefix=(hd0,6)/boot/grub insmod normal normal   UPDATE 4  Well, it seems like it is a requirement to boot into Linux. After booting into Ubuntu I have performed the following steps described in the :  sudo update-grub sudo grub-install /dev/sda   This did not resolve the issue. I still get the grub rescue prompt. What do I need to do to permanently fix it?  I have also learned that drive numbers as in hd0 need to be translated to drive letters as in /dev/sda for some commands. hd1 would be sdb, hd2 would be sdc, and so on. Partitions listed in grub as (hd0,msdos6) would be translated to /dev/sda6.  UPDATE 5  I could not figure out why the following did not fix grub:  sudo update-grub sudo grub-install /dev/sda   So I downloaded  based on an answer from  post. That seemed to do the trick after I picked the "Recommended Repair (repairs most frequent problems)" option. Picklist dependent on 2 controlling picklist I have 3 picklist in an object Test1, Test2, Test3  1. Test2 is dependent on Test1  2. Test3 is dependent on both.. Test1 and Test2    I want to have Test3 picklist showing values accordindly. i.e  if U selected Test1 = First and Test2 = SA . I should be able to see "IST,ABC and PQR" in Test 3.   Is this possible??? What's the best way to use matching methods with multiple treatment groups? I'm assessing the impact of an intervention on an outcome. For my first analysis, I used the MatchIt package (see code below) to match treatment and control groups and to compare outcomes for the treated vs control. The Treat variable is 0 or 1.  nn_match &lt;- matchit(treat ~ cov1 + cov2+ cov3 ,                      method = "nearest", data = df)   In my second analysis, I'd like to assess the effect of different treatment levels (for example, I have Treatment A, Treatment B, and Treatment C) on the outcome, but I'm stuck on the best way to proceed. Does it make sense to run separate matching analysis for each treatment group while excluding the observations from the other treatments groups?   nn_treatA_match &lt;- matchit(treat_A ~ cov1 + cov2+ cov3 ,                      method = "nearest", data = df_minus_other_treatBC) nn_treatB_match &lt;- matchit(treat_B ~ cov1 + cov2+ cov3 ,                      method = "nearest", data = df_minus_other_treatAC)   Or is there a way to run the analysis with the entire dataset and match controls to each treatment at the same time? Other posts have mentioned the twang package, but I'm not sure if that's what I should go with as I'd like to compare outcomes for each treated group to the control and not just across treated groups. Prove that $(a + b + c)^{13}$ is divisible by $abc$ if $b|a^3$, $c|b^3$ and $a|c^3$. Which are the word orders that can be found in English? I am attempting to add a calendar to my Default.aspx in my sharepoint hosted add-in in visual studio. I used the default code-snippet for adding sharepoint lists. Here's what I added to my Default.aspx:    &lt;WebPartPages:WebPartZone runat="server" FrameType="Default" ID="full" Title="loc:full"&gt;     &lt;WebPartPages:XsltListViewWebPart runat="server"         ListUrl="Lists/Calendar"         IsIncluded="True"         JsLink="clientTemplate.js"         NoDefaultStyle="TRUE"         PageType="PAGE_NORMALVIEW"         Default="False"         ViewContentTypeId="0x"&gt;     &lt;/WebPartPages:XsltListViewWebPart&gt; &lt;/WebPartPages:WebPartZone&gt;     and this is the result...    Pretty dang ugly if you ask me. How can I get this looking like a normal share point calendar instead of an unusable mess?  Thank you! Are punches with Gauntlets of Ogre Strength magical, improvised weapon attacks? My Gnoll Paladin just got the Gauntlets of Ogre Strength from Phandelver the other day, and it got me wondering:    Would it be possible/make sense for punches using them to count as an improvised weapon? (Since I'm not punching with empty fists, I'm wearing magical gauntlets) If so, would punches from a person using them count as magical weapon damage? PHP function overloading I need to start by stating that I have read through every single problem on here relating to mine, but all of them seem to have access somehow to their server's files. I do not, so here is my question.  I'm on centOS 6.5 and ssh closes connection right after a successful login. I am using mac and windows/putty to access my server with the same results. Is there anyway I can access my server now without having access to its files?   Below is the readout from ssh -vvv right after a successful login:  debug1: Authentication succeeded (password). Authenticated to 4X.5X.XX.2 ([4X.5X.XX.2]:82). debug1: channel 0: new [client-session] debug3: ssh_session2_open: channel_new: 0 debug2: channel 0: send open debug1: Requesting no-more-sessions@openssh.com debug1: Entering interactive session. debug2: callback start debug2: fd 3 setting TCP_NODELAY debug3: ssh_packet_set_tos: set IP_TOS 0x10 debug2: client_session2_setup: id 0 debug2: channel 0: request pty-req confirm 1 debug1: Sending environment. debug3: Ignored env TERM_PROGRAM debug3: Ignored env SHELL debug3: Ignored env TERM debug3: Ignored env TMPDIR debug3: Ignored env Apple_PubSub_Socket_Render debug3: Ignored env TERM_PROGRAM_VERSION debug3: Ignored env TERM_SESSION_ID debug3: Ignored env USER debug3: Ignored env SSH_AUTH_SOCK debug3: Ignored env __CF_USER_TEXT_ENCODING debug3: Ignored env PATH debug3: Ignored env PWD debug1: Sending env LANG = en_US.UTF-8 debug2: channel 0: request env confirm 0 debug3: Ignored env XPC_FLAGS debug3: Ignored env XPC_SERVICE_NAME debug3: Ignored env SHLVL debug3: Ignored env HOME debug3: Ignored env LOGNAME debug3: Ignored env _ debug2: channel 0: request shell confirm 1 debug2: callback done debug2: channel 0: open confirm rwindow 0 rmax 32768 debug2: channel_input_status_confirm: type 99 id 0 debug2: PTY allocation request accepted on channel 0 debug2: channel 0: rcvd adjust 2097152 debug2: channel_input_status_confirm: type 99 id 0 debug2: shell request accepted on channel 0 Last login: Wed Oct  7 06:23:21 2015 from 1XX.XXX.X1.185 debug1: client_input_channel_req: channel 0 rtype exit-status reply 0 debug1: client_input_channel_req: channel 0 rtype eow@openssh.com reply 0 debug2: channel 0: rcvd eow debug2: channel 0: close_read debug2: channel 0: input open -&gt; closed debug2: channel 0: rcvd eof debug2: channel 0: output open -&gt; drain debug2: channel 0: obuf empty debug2: channel 0: close_write debug2: channel 0: output drain -&gt; closed debug2: channel 0: rcvd close debug3: channel 0: will not send data after close debug2: channel 0: almost dead debug2: channel 0: gc: notify user debug2: channel 0: gc: user detached debug2: channel 0: send close debug2: channel 0: is dead debug2: channel 0: garbage collecting debug1: channel 0: free: client-session, nchannels 1 debug3: channel 0: status: The following connections are open:   #0 client-session (t4 r0 i3/0 o3/0 fd -1/-1 cc -1)  Connection to 4X.5X.XX.2 closed. Transferred: sent 3176, received 2640 bytes, in 0.3 seconds Bytes per second: sent 10370.6, received 8620.4 debug1: Exit status 254 Powershell Rename Multiple Files with LastWriteTime Prefix I am trying to put together a Powershell script that will:  -Search recursively from a root directory -Exclude files with existing "yyyyMMdd " file name prefix -Rename the files not excluded above with ""yyyyMMdd " file name prefix based on their specific LastWriteTime  Note: ideally, this script should include all file type extensions  I have tried myself, but it would seem to be above my head, as my attempts are not going well.  Thanks, in advance.    #StampMe.ps1 param( [string] $fileName)  # Check the file exists if (-not(Test-Path $fileName)) {break}  # Display the original name "Original filename: $fileName"  $fileObj = get-item $fileName  # Get the date $DateStamp = get-date -uformat "%Y-%m-%d@%H-%M-%S"  $extOnly = $fileObj.extension  if ($extOnly.length -eq 0) {    $nameOnly = $fileObj.Name    rename-item "$fileObj" "$nameOnly-$DateStamp"    } else {    $nameOnly = $fileObj.Name.Replace( $fileObj.Extension,'')    rename-item "$fileName" "$nameOnly-$DateStamp$extOnly"    }  # Display the new name "New filename: $nameOnly-$DateStamp$extOnly"   I am hoping to change the line:  $DateStamp = get-date -uformat "%Y-%m-%d@%H-%M-%S"   To be LastWriteTime instead of get-date, but I have no idea how to make this happen.  This code (from another Super User question):  Get-ChildItem "Test.pdf" | Rename-Item -newname {$_.LastWriteTime.toString("yyyyMMdd") + " Test.pdf"}   ...successfully renames a single file, but I can't seem to integrate this into the larger script.    With regards to running the above recursively, I have tried this (also from ):  foreach ($file in get-ChildItem *.* -recurse) { ./StampMe.ps1 $file.name }   Which succeeds to apply the PS script to files in the root directory, but fails to apply to any files in the sub-folder tree that propagates from the root directory. Is there a printable version of a reference manual for all TeX primitives? Can I estimate remaining battery life by measuring its voltage with the same MCU that it powers? I'd like to estimate the remaining battery life of a battery that powers a microcontroller. Could I accomplish this by simply leading the battery into the MCU's built-in ADC?  My idea is that I could plot the voltage over time to figure out how much battery life remains. But would the change in voltage be noticeable? And would it be a problem that the same battery powers the MCU (and ADC)? Value passed with request.setAttribute() is not available by request.getParameter() While using Wild Shape, do I use Unarmored Defense or the creature's Armor Class?