NDSolve with Piecewise solving BVP gives warning bvdisc
Can NDSolve handle discontinuous data?
I recently got my Blacksmithing skill to 100. Now in the skills menu I can press space to make it Legendary, which will put it back to a skill level of 15 and reset my perks.  I am wondering: What benefit is there from making a skill Legendary apart from being able to level up the skill more thus having infinite levels? After trying to delete apache and tomcat, and now trying to reinstall apache 2, I am missing the init.d/apache2 file to start/stop my server.  I am not sure if the new install actualy worked, and my apt-get purge apache2 didn't remove everything in the first place!  How can I get the init.d/apache2 file to test if server starts / is installed properly (I had removed files and directories manually)? Always return data from last week's Monday thru Sunday I am trying to set multiple definition queries for one layer based on one field using python.  ie.  I have a City layer with a field that holds the city name.  I want a copy of the layer in an MXD with the Definition query set for each value in the City field.  So essentially, I have one source layer, with a copy of the layer as many times as there are values in the City field.  The query would look like this: CITY = 'Atlanta' How do I remove/delete a folder that is not empty? Determine the number of functions $f: \{1,2,3....,1999\}\to \{2000,2001,2002,2003\}$satisfying the condition that $f(1)+f(2)+...f(1999)$ is odd. Problems:Determine the number of functions $$f: \{1,2,3....,1999\}\to \{2000,2001,2002,2003\}$$ satisfying the condition that $f(1)+f(2)+...f(1999)$ is odd.   My Attempt: Each integer in domain has $4$ choices and therefore the total number of functions is $f$ is $4^{1999}.$ Since there are an equal number of functions that yield odd or even result, we can directly write that the number of functions satisfying the above condition to be $2*4^{1998}.$ I am unsure about this last claim and would like to prove it (if it is true.)Also is the answer to this problem correct?  Edit $1$: I tried to proceed further in the following manner:   For a given mapping $f$ let the number of integers assigned to $2000,2001,2002$ amd $2003$ be $p,q,r$ and $s$ respectively, where $p,q,r,s\in \mathbb{Z}^+$. Therefore the sum in question can be written as $f(1)+f(2)+...+f(1999)=2000p+2001q+2002r+2003s.$ Clearly the sum will be odd iff $q+s$  is odd. Also note that $p+q+r+s=1999\Rightarrow p+r$ is even. On the other hand if we let $q+s$ as even then $p+r$ must be even. Now the number of values of $p,q,r$ and $s$ for which the above two lemmas hold is the same and therefore if we let $f$ to be the function which maps elements form $\{1,2,3,...,1999\}$ to $\{2000,2001,2002,2003\}$ such that $q+s$ is even and $g$ to be the function  hich maps elements form $\{1,2,3,...,1999\}$ to $\{2000,2001,2002,2003\}$ such that $p+q$ is even we will get a bijection.(Maybe!) Simple explanation to the induction from the slowly changing $\vec B$ of a solenoid in the region of $0$ magnetic field How to dynamically create a local variable? Let $f: \mathbb R^2 \to \mathbb R$ defined as   $f(x,y)=(x^2+y^2)\sin(\dfrac{1}{\sqrt{x^2+y^2}})$ if $(x,y) \neq (0,0)$, $f(x,y)=(0,0)$ if $(x,y)=(0,0)$  Prove that $f$ is differentiable at $(0,0)$ but that the partial derivatives of $f$ are not continuous at the origin.  The attempt at a solution:  I had some problems at the first part of the exercise:  I've calculated $\dfrac{\partial f}{\partial x}(0,0)$ and $\dfrac{\partial f}{\partial y}(0,0)$, both exist and are equal to $1$.  So, to prove $f$ is differentiable at the origin, I have to show that   $\lim_{(x,y) \to (0,0)} \dfrac{|f(x,y)-(f(0,0)+&lt;\nabla f(0,0),(x,y)&gt;)|}{\|(x,y)\|}=0$ But $\lim_{(x,y) \to (0,0)} \dfrac{|f(x,y)-(f(0,0)+&lt;\nabla f(0,0),(x,y)&gt;)|}{\|(x,y)\|}$ equals  $\lim_{(x,y) \to (0,0)} \dfrac{|(x^2+y^2)\sin(\dfrac{1}{\sqrt{x^2+y^2}})-(x+y)|}{\|(x,y)\|}$. I don't know how to show this limit equals $0$.  For the second part (I've only analyzed $\dfrac{\partial f}{\partial x}$ since both cases are the same), what I did was try to show that $\lim_{(x,y) \to (0,0)} \dfrac{\partial f}{\partial x}(x,y) \neq \dfrac{\partial f}{\partial x}(0,0)$   I thought of considering the curve $\phi(t)=(t,0)$, so   $\lim_{t \to 0} (f\circ \phi)(t)=\lim_{t \to 0} 2t\sin(|t|^{-1})-\dfrac{t\cos(|t|^{-1})}{|t|^{-1}}$. But $\lim_{t \to 0^{+}} \dfrac{t\cos(|t|^{-1})}{|t|^{-1}}=\lim_{t \to 0^{+}} \cos(\dfrac{1}{t})$ and this limit doesn't exist, so the original limit doesn't exist. This shows the partial derivative with respect to $x$ at the point $(0,0)$ is not continuous.   I would appreciate if someone could help me to finish the first part and tell me if what I did in the second part of the problem is correct. com.mysql.jdbc.exceptions.jdbc4.CommunicationsException: Communications link failure I read this book once when I was in middle school. A girl solves a murder or a mystery on a spaceship. It was a thin paperback books.   All I can remember is that there was an alien, and there was a movie star or actress or famous makeup artist on the ship traveling with another woman. By the end of the book the murderer was the woman the actress was traveling with who forced her to use her makeup skills to disguise her, and she was really some kind of alien. If you give a user sudo privileges how can I remove the sudo privileges and make the user become just a regular user?  I used:  sudo adduser username sudo   Now I've changed my mind. How to avoid bad box with long words with no hyphenation? I wanted to leave the question title as is so as not to take away from my amusement :).  Anyway,     It's raining.   What is raining? Is it the sky? The clouds? The weather? The rain? What is "it"? Any historical insights on the statement? Can Spirit Guardians affect enemies through walls? What's the canonical way to check for type in Python? What are these circular splotches on my negatives? Is this mold? Black? White? Guys I need to find out what this is- it's also on my wooden bed racks Are there any method to extend a filesystem when i adding more hdd to it without using LVM? What are those ? How unique is the php session id