Is it possible for a function to be continuous and differentiable in an interval, but its derivative over that interval is not continuous?
How would I give a simple example of a function $f$ differentiable in a deleted neighborhood of $x_0$ such that $\lim_{x\to x_0}f^\prime(x)$ does not exist? I cannot seem to think of an example.  A delete neighborhood is an open interval about $x_0$ which does not contain $x_0$. So, $(x_0-\delta,x_0+\delta)-\{x_0\}$ for some $\delta&gt;0$.  How would something be differentiable in a deleted neighborhood if at the point of the derivative, the limit does not exist. Presumably, the derivative ends up looking something like $\lim_{x\to x_0} \dfrac{1}{x}$, if it does not exist.
Need to draw a flowchart as in the image below with some arrows I have problem with the feed back from bottom block to on top of top block. Can anyone help? How to determine whether the direction of rotating a 2D vector to another one is counter-clockwise or clockwise using the cross product? Vec2 a, b; // some random vector Vec2 cross = a.Cross(b); RelativeDirection(a,b,cross); // return true if the direction of                               // rotating a to b is counter-clockwise   How do I implement the function RelativeDirection()?  I got some suedo code from the textbook:  if a.Cross(b) &gt; 0 then ... else ...   but the cross product is a vector right? how do you compare it with an integer? Non constant analytic function from $\{z\in\mathbb{C}:z\neq 0\}$ to $\{z\in\mathbb{C}:|z|>1\}.$ I just bought all the ingredients to make a soup in the crock pot. I was planning on having it cook all day, but I just realized the recipe only calls for it to cook on low for 3-4 hours. If I cook it on low for 3-4 hours, and then put it on warm before I leave for work, will it be a bacteria minefield or will it be warm enough to keep the food safe from bacteria? If a,b,c,d are positive integers with a sum of 63, what is the maximum value of ab + bc + cd ? (By using calculus to solve it)) If $a,b,c,d$ are positive integers with    $$a+b+c+d=63,$$   what is the maximum value of $$ab+bc+cd?$$   I treated this as an optimization problem and tried to solve it but I did not make any progress. I am considering buying my first DSLR.  How do I know whether I need a 18-200 lens, 17-85, or 18-55? Or something else? Pronunciation differences between "finite" and "infinite" In my experience, "finite" is pronounced (IPA) ˈfaɪnaɪt while "infinite" is ˈɪnfɪnɪt.  In general, the prefix "in" negates an adjective, but does not change the pronunciation. Based on this, I would expect ˈɪnfaɪnaɪt.  Is there a reason for this "deviation from the norm"? Are there dialects/regions that actually say ˈɪnfaɪnaɪt (or ˈfɪnɪt, for that matter)? How to test apex classes with Pagereference? I'm struggling to test a class with pagereference. Following is the class...  public with sharing class redirectOrderPartner{  public String currentRecordId {get;set;} public orders__c orderId {get;set;}  public redirectOrderPartner(ApexPages.StandardController controller) {      }     Public Pagereference go(){      currentRecordId  = ApexPages.CurrentPage().getparameters().get('orderid');      system.debug('---currentRecordId  ---'+currentRecordId  );     orderId = [select id from orders__c where name =: currentRecordId limit 1];      system.debug('---orderid---'+orderId);      PageReference pageRef = new PageReference('/apex/OrderTrackingClass?id='+orderId.id);     pageRef.setRedirect(true);     return pageRef;    }   }   Following is what I tried....    @isTest  public class redirectOrderPartner_TEST  {             static testMethod void Test(){            Account acc = new Account(Name='ABC Corp.');           insert acc;            orders__c tempOrder = new orders__c(name = '0001234567', account__c = acc.id );           insert tempOrder;            Test.startTest();            PageReference pageRef = Page.redirectOrderPartner;           Test.setCurrentPage(pageRef);            ApexPages.Standardcontroller sc = new ApexPages.Standardcontroller(tempOrder);           ApexPages.currentPage().getParameters().put('Id',tempOrder.name);           PW_redirectOrderPartner ec = new redirectOrderPartner(sc);           ec.go();                                   Test.stopTest();       }   } I get the following error message on testing..     System.QueryException: List has no rows for assignment to SObject   What am I missing? Thanks Where can I find legendary crafting materials? What item bonuses apply to my follower? There are a lot of different side effects an item can have, and I assume that things like magic find have no influence on any of "our" found items at all.  However, I'm not sure about other things. For example:   Do followers get life-steal on weapons, too? Does increased orb healing make any difference? What about +experience after kills? Will my follower level up faster?   and probably a lot more.  Is there some general rule as to what effects of an item apply to followers, and which don't? How would I go about creating a 3D MMORPG Mouse Look? How would I go about creating a 3D MMORPG Mouse Look? I have created a 3D Space Rpg that is almost finished with success so far. However, I didn't have a clue, how I would attempt to make a Mouse Look method where if a user right clickes and then holds the right mouse button and moves it around the camera moves around with the mouse. The camera can not move away from your character/ship, it should act as if the character/ship is it's origin and that it rotates all around the origin.  I don't mind coding this with python either. Advice is welcome! Awesome symbols and characters in a bash prompt I just ran across a screenshot of someone's terminal:    Is there a list of all of the characters which can be used in a Bash prompt, or can someone get me the character for the star and the right arrow? Join matrix based on conditions Tsunami dampening mechanisms Windows says RAM ran out while there is still 4 GB of physical memory available I'm just wondering how it is possible that IGN.com has this in its title tag:      Video Games, Cheats, Walkthroughs, Game Trailers, Reviews, News, Previews &amp; Videos at IGN   while on Google its title is simply "IGN".   How can one achieve such a thing? Does it use some special meta tag I can't see? Prove the $n$th Fibonacci number is the integer closest to $\frac{1}{\sqrt{5}}\left( \frac{1 + \sqrt{5}}{2} \right)^n$ Prove that the $n$th Fibonacci number $f_n$ is the integer that is closest to the number $$\frac{1}{\sqrt{5}}\left( \frac{1 + \sqrt{5}}{2} \right)^n.$$   Hi everyone, I don't really understand the problem. I have the following hint, but I don't know how to work it.     Hint: Show that the absolute value of $\frac{1}{\sqrt{5}}\left( \frac{1 - \sqrt{5}}{2} \right)^n$ is less than $1/2$. Why does the CAN bus use a 120 ohm resistor as the terminating resistor and not any other value? I have embedded a Python interpreter in a C program.  Suppose the C program reads some bytes from a file into a char array and learns (somehow) that the bytes represent text with a certain encoding (e.g., ISO 8859-1, Windows-1252, or UTF-8).  How do I decode the contents of this char array into a Python string?  The Python string should in general be of type unicode—for instance, a 0x93 in Windows-1252 encoded input becomes a u'\u0201c'.  I have attempted to use PyString_Decode, but it always fails when there are non-ASCII characters in the string.  Here is an example that fails:  #include &lt;Python.h&gt; #include &lt;stdio.h&gt;  int main(int argc, char *argv[]) {      char c_string[] = { (char)0x93, 0 };      PyObject *py_string;       Py_Initialize();       py_string = PyString_Decode(c_string, 1, "windows_1252", "replace");      if (!py_string) {           PyErr_Print();           return 1;      }      return 0; }   The error message is UnicodeEncodeError: 'ascii' codec can't encode character u'\u201c' in position 0: ordinal not in range(128), which indicates that the ascii encoding is used even though we specify windows_1252 in the call to PyString_Decode.  The following code works around the problem by using PyString_FromString to create a Python string of the undecoded bytes, then calling its decode method:  #include &lt;Python.h&gt; #include &lt;stdio.h&gt;  int main(int argc, char *argv[]) {      char c_string[] = { (char)0x93, 0 };      PyObject *raw, *decoded;       Py_Initialize();       raw = PyString_FromString(c_string);      printf("Undecoded: ");      PyObject_Print(raw, stdout, 0);      printf("\n");      decoded = PyObject_CallMethod(raw, "decode", "s", "windows_1252");      Py_DECREF(raw);      printf("Decoded: ");      PyObject_Print(decoded, stdout, 0);      printf("\n");      return 0; } Fix terminal after displaying a binary file