If $f(x) = f(2x)\forall \; x \in \mathbb{R}$ and $f(x)$ is continuous for all $x\in \mathbb{R}$ and $f(5) = 10,$ Then $f(2016) = $   $\bf{My\; Try::}$ Let $0&lt;x&lt;1$  Then $f(x)=f(2x) = f(2^2x) = f(2^3x)=......=\lim_{n\rightarrow \infty}f(2^nx) = f(0)=\bf{Constant}$  and when $x&gt;1$  Then $\displaystyle f(x) = f\left(\frac{x}{2}\right) = f\left(\frac{x}{2^2}\right)=f\left(\frac{x}{2^3}\right)=.......=\lim_{n\rightarrow \infty}=f\left(\frac{x}{2^n}\right)=f(0)=\bf{Constant}$  But I did not understand How can we solve for $x&lt;0$ and $x=0$ and for $x=1$  Help Required, Thanks
If a Continuous function $f(x)$ satisfies $f(x) = f(2x)$, for all real $x$, then does $f(x)$ necessarily have to be constant function? If so, how do you prove it? If not any counter examples?
doesn't has to /have to Most games build on other games' successes and many are downright clones. Where is the limit of imitation before legal issues come into play? Is it down to literary or graphic work like characters and storyline that cause legal problems, or can someone actually claim to own gameplay mechanics?  There are so many similar clone games out there that the rules are probably very slack or nonexistent, but I'd like to hear the views of more experienced developers / designers. How to view CD key for a Steam game? I have purchased a game on Steam and can not find out the details of the file or purchase. How does one find their CD Key from a game purchased in Steam? How to read ext4 partitions in Windows? I have two questions on ext4:   Is there currently a way to mount an ext4 partition in Windows (XP/Vista/7) to get basic read support? If not, are there any plans to support this someday? What's the action of banging two beers together called? Change date format [YYYYMMDD] to [MM/DD/YYYY] I generated a report that formats date as 20160509 and my Google Sheets locale is already set to United States. I've played around with various options within Format > Number > Date Format but I can't change the dates to MM/DD/YYYY format without doing a simple find and replace. How do I accomplish this? It appears that in anticipation of D&amp;D Next Wizards of the Coast has removed much of the Dungeons and Dragons, 3rd Edition Web content. I didn't perform a thorough search to determine if all the content is removed (e.g. I know the Three Dragon Ante Web enhancement  and the Mind's Eye column about psionic tattoos  are both gone--better not to ask why those are my go-to articles), but it all might be.  What's the best way--and by best I mean both legal and convenient--to continue to access this content? We know that $221 = 17*13$. So we can check if the system has roots to both of those equations separately, which it does:  $x^{5} \equiv 2$ mod $13$ has the solution $6 + 13n$ and $x^{5} \equiv 2$ mod $17$ has the solution $15 + 17n$.   I got these numbers from wolfram, I have no idea how to solve this problem WITHOUT a calculator. And even after finding these numbers. How would one obtain a solution modulo $221$? I was thinking the Chinese Remainder Theorem but I am under the assumption that CRT only applies to problems with powers of $x$ which are $1$.  Thanks. Desperate to locate and re-read exceptional book/series, but cannot remember the title. The high concept: The U.S. has just sent the first successful expedition to Mars, and it has just landed. As the astronauts make their initial exploration outside their ship, a tear in the fabric of space opens up right in front of them, and they look through to the insides of a laboratory (at a California university?) and two students who just figured out how to create arbitrary portals between two points in the Universe. The rest of the novel/series is a consequence of this breakthrough. But I can't remember the author and title(s). Surely someone reading this forum will remember it well! TIA.  (Reposted .) AttributeError: MapDocObject: Unable to save on mxd.save/saveACopy? I'm trying to use arcpy to save an .mxd and am having an issue.  It doesn't matter if I use mxd.save or mxd.saveACopy I get the same error.  I know it doesn't look like I am doing anything w/ it here, but it's just a portion of my code:  import arcpy import arcpy.mapping as map arcpy.env.overwriteOutput = True  env.workspace = r"C:\MGIS\FinalProject2.gdb     mxd = map.MapDocument(r"C:\MGIS\Finalproject2.mxd") df = map.ListDataFrames(mxd)[0]  for df in map.ListDataFrames(mxd): df.scale = 2000000  #Add layers into map document addLayer = map.Layer(OKXcounties) addLayer1 = map.Layer(contourLabelText) addLayer2 = map.Layer(contoursClipLyr) addLayer3 = map.Layer(clipOKXLyr) map.AddLayer(df, addLayer, "AUTO_ARRANGE") map.AddLayer(df, addLayer1, "AUTO_ARRANGE") map.AddLayer(df, addLayer2, "AUTO_ARRANGE") map.AddLayer(df, addLayer3, "AUTO_ARRANGE")  # Add contour Labels for lyr in map.ListLayers(mxd):     if lyr.name == "contourLabelText":         lyr.showLabels = True     if lyr.name == "Contour Features":         lyr.transparency = 100  mxd.saveACopy(mxd)   I get the following error:   Traceback (most recent call last):   File "C:\Python26\ArcGIS10.0\Lib\site-packages\pythonwin\pywin\framework\scriptutils.py", line 312, in RunScript     exec codeObject in __main__.__dict__   File "C:\MGIS\geog485\FinalProject2\mxdtest.py", line 7, in &lt;module&gt;     mxd.saveACopy(mxd)   File "C:\Program Files\ArcGIS\Desktop10.0\arcpy\arcpy\utils.py", line 181, in fn_     return fn(*args, **kw)   File "C:\Program Files\ArcGIS\Desktop10.0\arcpy\arcpy\_mapping.py", line 668, in saveACopy     self._arc_object.saveACopy(file_name) AttributeError: MapDocObject: Unable to save.  Check to make sure you have write access to the specified file and that there is enough space on the storage device to hold your document.   Space is not the issue, I have 60 GB of free space and I've checked the windows properties of the .mxd file.  Read-only box is unchecked and I've "allowed" all permissions for all groups:    Does anyone have any idea how if this is a bug or how I can fix this?  I'm using ArcInfo 10.0 SP4. Why does it take so long to review a flag suggested by a user? Why does it take so long to review a flag suggested by a user?  When I flag a question or comment, some get a response quickly whereas some of them get a response after few or more hours.  Is there any flag review condition which cause so much time to be taken for different flags?  Or are there different moderators for different flag posted? Do ground seeds contain oil? Deleting array elements in JavaScript - delete vs splice I have created a VF page and used "render as pdf"  &lt;apex:commandButton value="Save to Opportunity" action="{!savePdf}"  /&gt;   Its working fine when i am using above line without rerender and oncomplete but when i am adding rerender or oncomplete it is not working.I am able to save the PDF in attachment folder but when i am trying to open its showing  "Unable to load document"  Even if i remove oncomplete and use Rerender then also its saving the attachment in Attachment object and when i view ,it is not loading and says "Unable to load document"      &lt;apex:commandButton value="Save to Opportunity" action="{!savePdf}"  oncomplete="myClose();"/&gt;   Javascript Code  function myClose(){      self.close();     window.opener.location.href="/{!$CurrentPage.parameters.Id}";  }   Class Code  public void savePdf() {      PageReference pdf = Page.GenerateQuotePDF;     pdf.getParameters().put('id',parentId);      Attachment attach = new Attachment();      Blob body;     body = pdf.getContent();     attach.Body = body;     attach.Name = 'Opportunity'+ '.pdf';       attach.IsPrivate = false;     attach.ParentId = parentId;     attach.ContentType = 'application/pdf';     insert attach;     }     Please help.. How to give an image or video a TV screen effect? I've upgraded from 12.04 to 14.04 via command-line when my system froze, had to do REISUB and dpkg --configure -a to recover from crash after rebooting.  Now everything seems to work except automatically mounting external thumb drives and external hard disk drives. After plugging in said drives, they fail to show up on the left pane and remains unmounted. I can see the device if I run lsusb and fdisk though, so it's possibly to manually mount it but I'd rather resolve why it's not automatically mounting. Subgroups of Symmetric groups isomorphic to dihedral group Is $D_n$, the dihedral group of order $2n$, isomorphic to a subgroup of $S_n$ ( symmetric group of $n$ letters) for all $n&gt;2$? After writing code to populate textboxes from an object, such as:  txtFirstName.Text = customer.FirstName; txtLastName.Text = customer.LastName; txtAddress.Text = customer.Address; txtCity.Text = customer.City;   is there way in Visual Studio (or even something like Resharper) to copy and paste this code into a save function and reverse the code around the equal sign, so that it will look like:  customer.FirstName = txtFirstName.Text; customer.LastName = txtLastName.Text; customer.Address = txtAddress.Text; customer.City = txtCity.Text; How do I write content to another browser window using Javascript? I've opened a new window with window.open() and I want to use the reference from the window.open() call to then write content to the new window.  I've tried copying HTML from the old window to the new window by using myWindow.document.body.innerHTML = oldWindowDiv.innerHTML; but that's doesn't work.  Any ideas? Physically Identify the failed hard drive