I am studying now calculus and I am learning about hyperbolic function. But I can't understand why hyperbolic functions are called 'hyperbolics' Is there any relation between hyperbolic function and hyperbola? And why there are natural constant e in function? I saw some information that notices the relation between them in Wikipedia, so I try to find the relation as integrating the hyperbola, but I can't solve that. Please tell me why they are called 'hyperbolic' and derivate the hyperbolic function. (If the hyperbolic function is just defined so, please tell me why they are defined so.)
I don't really get why these hyperbolic functions are named after trig functions. Can someone enlighten me?
How come SG-1 couldn't get back to Earth? What is the command to open the shutdown dialog? I would like to use a gesture to shutdown/restart my computer and I need to know the command that launches the shutdown dialog: What does the factorial of a negative number signify? I understand that the factorial gives the number of arrangements. For example: the factorial of zero i.e. an empty set ( doesn't occur) is 1.   As the empty set can be arranged only in 1 way - i.e. by filling nothing. Now, let's take an example: 5 distinct seats. How many ways 5 distinct seats can be arranged? - 5! ways i.e. 120.  So, basically, factorial gives us the arrangements. Now, the question is why do we need to know the factorial of a negative number?, let's say -5. How can we imagine that there are -5 seats, and we need to arrange it? Something, which doesn't exist shouldn't have an arrangement right? Can someone please throw some light on it?. I saw some research done on the formula - I’m looking for a word I’m struggling to remember that refers to a job or role which is inconsequential and usually created in order to install someone in a company, not based on their merit.  An example would be creating a vague new role for a friend’s son. The word I’m looking for refers to the actual job itself - it’s a noun that would replace the ‘job’ (e.g “they put so and so’s cousin in a ____”).   I believe the word may not be a strictly formal or technical word but I don’t think it was slang. What would you consider to be the best exception type to throw when an extension method is called on a null instance (where the extension method does not allow it)? Since extension methods are nothing but static methods you could argue that it should be ArgumentNullException, but on the other hand they're used like instance methods so it might be more natural to use the NullReferenceException. Let's take the following example:  public static string ToInvariantString(this IFormattable value, string format) {     return value.ToString(format, CultureInfo.InvariantCulture); }   This way a NullReferenceException will be thrown if the value parameter is null.   The other example would be:  public static string ToInvariantString(this IFormattable value, string format) {     if (value == null) throw new ArgumentNullException("value");     return value.ToString(format, CultureInfo.InvariantCulture); }   EDIT: In some of the answers you have pointed out that an extension methods can be called like a static method and in those cases a null reference exception would be wrong, which is a great point, and actually one of my concerns, not sure why I forgot to mention that in the question in the first place.   Someone also pointed out that it's wrong to throw a NullReferenceException, and yes, it is. That's why I don't throw it, I just let it happen (let the CLR throw it) by not guarding the method.  I think I favor the ArgumentNullException (that's what I've use so far) but I still think there is at least room to argue for an against the NullReferenceException since it seems more natural in most places where the method is going to be used. How do you switch from Wayland back to Xorg in Ubuntu 17.10? Some of my applications don't work on Ubuntu 17.10 Wayland. How can I switch back to Xorg? Applying options to already loaded package Is there a way to apply some options to a package which is loaded in the cls file I am using? For instance, suppose that the cls file loads graphicx, and I want to apply the option demo to it from my tex file. How to create quizzes with macqtex? Identify this YA book series about dragons, acid blood, and dangerously cold nights I'm trying to remember the name of a series of books about a boy who works with dragons.  Dragon's blood (or maybe it was slobber?) is acidic, and the children who wrangle these dragons often end up with deep pock marks.  On this world, days are like ours but nights get very cold, requiring anyone stuck outside to find a shelter until dawn (not the false dawn)  The other thing I remember is that in one of the books by slicing open a dragon and spending the night, the character emerged with special dragon powers. What's the best way to return multiple values from a function? I have a function where I need to do something to a string.  I need the function to return a boolean indicating whether or not the operation succeeded, and I also need to return the modified string.    In C#, I would use an out parameter for the string, but there is no equivalent in Python.  I'm still very new to Python and the only thing I can think of is to return a tuple with the boolean and modified string.  Related question: Keep processes running after SSH session disconnects Broken "Network profile" link when Area51 is their only account In ArcMap, when you export data to PDF it preserves the layering within the PDF so that you can turn on/off individual map layers (within the PDF itself).  When I export from QGIS to PDF, I don't appear to have the option for this.  Does QGIS support preserving layers when exporting to PDF?  Is there a special setting needed to enable this capability?  Or has anyone wrote a plugin for this feature? I want to know how to format a storage drive from the terminal. Helpful things to provide in the answer would be often used options for commands and base knowledge that one can use to extrapolate future uses. Specifically I would like to know how to format in the different file systems such as NTFS, FAT32, EXT4, etc. Information on how to partition the drive via terminal is also wanted.  I am trying to format a high capacity external hard drive (EHDD) into NTFS - from the terminal.   I know I can use gparted for this as well as other GUI programs, but I still want to now how to do it from the terminal. I'm trying to use biblatex and when I compile my document I get an error like the following:  Windows  data source C:\Users\&lt;username&gt;\AppData\Local\Temp\par-5061756c\ cache-890efc00b3ca6b775c7d44a325c1349fb2a3a3bd\inc\lib/Biber/LaTeX/recode_data.xml not found in .   Mac  data source /var/folders/v2/rld0ls7d2935gkvqv5hfr1x00000gn/T/par-616c616e/ cache-cdd483146f82a9655ce063f848d5139480fbf872/inc/lib/Biber/LaTeX/recode_data.xml not found in .   Linux  data source /tmp/par-6963617269756d/cache-f37ab610b7d79b2720a8ee3732849c6821705520 /inc/lib/Biber/LaTeX/recode_data.xml not found in . How to tell the difference between linear and non-linear regression models? PHP __PHP_Incomplete_Class Object with my $_SESSION data How do I do this? I created a user without a home directory and now I want to create one. Not just a folder called new_user, I want the default home directory with all it's folders and hidden files, etc. I am reading separable extension. I don't quite understand why $\text{char} 0$ fields must be perfect. If $F$ is a $\text{char} 0$ field, $f(x)$ is an irreducible polynomial in $F[x]$. Then why $f$ must be separable? Assume $f$ has multiple roots, say $r$ is a multiple root of $f(x)$. Then $r$ is also a root of $f'(x)$. $r$ is in the splitting field of $f(x)$ over $F$, denote it as $E$. Then why $f$ must divide $f'$? I know $f$ is irreducible but I don't know how the argument goes on. Thanks for any help! Why does my front derailleur not work when it is cold? When it is warm outside my front derailleur works just fine. But when it gets colder (40F) the lever on the handle bar does not catch and I can move it without any resistance the whole way without the derailleur shifting.  Update: The wire is not moving and the shifter is a Shimano Deore.  Any idea what can cause that and how to fix it?