Let, $f(x,y)=|xy|$, Show that $f$ is differentiable at $(0,0)$   I started with by trying to prove $\lim_{h\to 0,k\to 0}\dfrac{f(0+h,0+k)-f(0,0)}{hk}$ exists. Then, $\lim_{h\to 0,k\to 0}\dfrac{|hk|}{hk}=\lim_{h\to 0,k\to 0}\dfrac{|h||k|}{hk}=\lim_{h\to 0}\dfrac{|h|}{h}\lim_{k\to 0}\dfrac{|k|}{k}$  Can I do this? Because, if I do this, $f$ may not be differentiable, but I have to show the converse. Thanks, for any help!
Is $f(x,y) = |xy|$ differentiable in $(0,0)$? I have no idea how to approach this problem.
Given an array of n Objects, let's say it is an array of strings, and it has the following values:  foo[0] = "a"; foo[1] = "cc"; foo[2] = "a"; foo[3] = "dd";   What do I have to do to delete/remove all the strings/objects equal to "a" in the array? Dynamic LINQ OrderBy on IEnumerable / IQueryable I found an example in the  for Dynamic LINQ that allows you to use a sql-like string (e.g. OrderBy("Name, Age DESC")) for ordering. Unfortunately, the method included only works on IQueryable&lt;T&gt;. Is there any way to get this functionality on IEnumerable&lt;T&gt;? How do you find the distance from a point to a plane? I am having trouble with this:      Find the distance from the point $(1,1,1)$ to the plane $2x+2y+z=0$.   Any ideas? Thanks. Preview of CAD files in format .dwg I'm looking for a utility or a program for Ubuntu, and possibly even for Windows that is able to convert a CAD file format .DWG to PDF.   My need is to provide a preview of CAD files, and I thought that the easiest way is to convert them into PDF format, but I'm open to suggestions, even if there is only the possibility to convert them to JPG image file type or PNG would be fine.  What interests me is only to find some solution, no matter if it is commercial or free I have an array in Perl:  my @my_array = ("one","two","three","two","three");   How do I remove the duplicates from the array? Story about a time-traveler living backwards in a capsule I'm hunting for the title of a short story where a senile old man appears in a capsule in a laboratory.  They eventually realize time is passing backwards for him. After years he helps them build the machine he's in, and he changes places with the him that has been aging normally in the timeline. Material setings in properties window is missing I have added a sphere and I was able to add material and give it a color. Now when I add a second sphere (separate object), the material panel is just blank. Is Python/ArcPy capable of delimiting strings with commas into different fields, and running a calculation based on those separate columns Using ArcGIS ArcMap 10.6: I have a text field in an attribute table that has comma separated values (example: 12,24, 64, 87,29). For this example, I will name this field VALUES. Please note that VALUES includes data collected from field work so the spacing between commas will be varied. My current workflow is as followed:  Export the ID and VALUES fields in the attribute table into a .csv file using Table to Table in ArcMap 10.6 Open the .csv in Excel and run the 'text to columns' function under the Data ribbon Separate the VALUES field into multiple columns based on commas Run the calculation: Copy Column I values and ID columns into a new .csv file Save and close the new .csv file and join the shapefile to the new .csv file based on ID Export the newly joined shapefile into a new file and delete the duplicate ID field in the new shapefile  I am wondering if there is a way to automate this Python/ArcPy so I can create a custom script tool to do this without leaving the ArcGIS environment. Is there a way to separate values in a text field based on commas into different columns, run the above calculation, and have the values from that calculation entered in a new field named VALUES_CALCULATED? Quaternions, Rotations and Real numbers I haven't really formally studied Algebra at anywhere near this level, but I was told about the existence of Quaternions a few years ago and I find them really cool. I also like how pure quaternions are analogous to cross products in $R^3$, and that it gives me a way of doing it algebraically rather than relying on hand rules.  Over the course of using them it's my understanding that multiplying an element by another, both imaginary numbers, rotates it in some manner so as to be orthogonal to both, similar to rotations of $\frac{\pi}{2}$ in the space with one real and one imaginary axis when multiplied by $i$, which is why it's useful for cross products as it will rotate it to be orthogonal to a plane spanned by linear combinations of those two vectors [afaik].   What I can't intuit though is why for any pure quaternion multiplication, there's a negative real part [the scalar product] if it's meant to correspond to a rotation within $R^3$ and the space of pure Quaternions is Isomorphic to $R^3$. Similarly I don't understand why $i^2 = j^2 = k^2 = $ A negative real. I have no idea how to find this integral:  $$\int_0^1\frac{(x-x^2)^4}{1+x^2}\ dx\ ?$$  Any help would be appreciated. Thanks in advance. How to calculate the sum of the data that have the same ID in the first column? I want to sum the values of the rows of my data that have the same ID in the first column. My data looks like   data.txt  Id    a    b    c    d    e 1     1    2    3    4    5 1     2    3    4    5    6 1     3    4    5    6    7 2     4    5    6    7    8 2     5    6    7    8    9 2     6    7    8    9    10 3     7    8    9   10    11 3     8    9    10  11    12 3     9    10   11  12    13 3     10   11   12  13    14 4     11   12   13  14    15 4     12   13   14  15    16 5     13   14   15  16    17 5     14   15   16  17    18   Required results  out.txt  Id    a     b   c   d   e 1     6     9   12  15  18 2     15    18  21  24  27 3     34    38  42  46  50 4     23    25  27  29  31 5     27    29  31  33  35 How to forward specific log file outside of /var/log with rsyslog to remote server? How can I forward message from a specific log file like /www/myapp/log/test.log with rsyslog client to remote rsyslog server? This log file is outside of the directory /var/log. After my , I've now got a new suggestion: down votes should not have any side effect in meta.  By side effects, I mean something like banning me from asking questions due to too many down votes, which I am experiencing right now:     states that I am permanently banned unless I improve my standing by posting some quality answers.  Seriously, I'm new to the site, and thus I'm not capable of posting quality answers on Meta.  So my only refuge was to create a new account. I think this check for previously downvoted posts should be disabled on Meta. I want to detect when someone is building a lever, then replace it with another lever that has the canplaceon tag so it can be placed on a redstone_lamp  How can I clear the crafting item and replace it with one that has a canplaceon tag? Interaction of Invoke Duplicity and Misty Step I am looking for a simple way to get a mime type where the file extension is incorrect or not given, something similar to  only in .Net. At work today, I came across the volatile keyword in Java. Not being very familiar with it, I found . Given the detail in which that article explains the keyword in question, do you ever use it or could you ever see a case in which you could use this keyword in the correct manner? Modify all bash commands through a program before executing them I am trying to create a program which require such feature. The flow will be like:   User enter a bash command User hit the enter My script will get command, current directory,.. as variables. Program can optionally modify the command. Modified command will get executed normally.   Is there any way to do this?  Note: I need this for my personal use, I am not going to distribute this program. How to imitate commercial fried chicken? I'm trying to develop my own "secret" fried chicken recipe, something that is similar to Popeye's or Church's. I'm a LONG ways from getting there. Here's what I did in my last experiment:   Chicken was marinated in buttermilk with Cajun spices and Tabasco sauce for 24 hours I used a deep fryer and canola oil. 175C. Prior to "dressing" the chicken, I let the excess buttermilk brine drip off the chicken. I then seasoned it with Cajun seasoning I made a batter using an egg, self rising flour, milk, baking powder I also tried using just plain flour for breading   Results:   Using the batter, the chicken came out looking burned and too smooth (didn't have that crunchy look). It burned too much that I couldn't finish cooking the chicken. Using the flour, the chicken came out with a thin crust, somewhat crispy, but also too burnt. Dipping the chicken in the batter AND then flour gave a bulky &amp; crunchy look. However, again, the result looked too burnt.   Modifications:  I then changed the the breading. I used bread flour and corn starch. I dipped the chicken in the batter again, then used the new breading. The bread flour was a bit lighter. And the corn starch was even more lighter. But they were still burn looking (just lighter shades). I also dropped the temperature to 160C.  Results:  Burnt chicken whose crust wasn't really sticking to the skin/meat.  Questions:  Any suggestions on what I can do to improve? I'm guessing something in the batter is causing the burnt coat. What flour should I use? What can I do to make the coat stick to the skin/meat? Any other suggestions on what to do? Authenticate to Stack Exchange using GitHub I've seen sign in methods using  as an authentication provider, for example : (AWS Cloud9)        Is it possible to authenticate into Stack Exchange using this method? At the moment there's other methods such as OpenID, Google, Yahoo and Facebook, but it would be interesting to also have the GitHub authentication.