
Math General Math Forum  For general math related discussion and news 
 LinkBack  Thread Tools  Display Modes 
May 22nd, 2017, 09:17 AM  #1 
Newbie Joined: May 2017 From: usa Posts: 1 Thanks: 0  Continuity of vectorial function
Hi every one. Let $\displaystyle f:\mathbb{R}^{*}_{+}\to\mathbb{R}$ a given function and $\displaystyle g:\mathbb{R}^2\to\mathbb{R}^2$ the function defined by: $\displaystyle g(x,y)=\begin{cases} (x,y) & \text{if $x\leq 0$}\\ (x,y+f(x)) & \text{if $x>0$} \end{cases}$ Questions: What is the condition on $\displaystyle f$ for: 1) The continuity of $\displaystyle g$ in $\displaystyle \mathbb{R}^2$? 2) The differentiability of $\displaystyle g$ in $\displaystyle \mathbb{R}^2$? 3) $\displaystyle g\in C^1$ Thank you. 

Tags 
class c1, continuity, differentiability, function, vectorial 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Continuity of a function  MathAboveMeth  Calculus  1  January 7th, 2017 03:55 AM 
Vectorial norm help  juanpe966  Calculus  4  February 27th, 2016 02:24 PM 
Continuity of a function.  condemath2  Calculus  6  June 6th, 2014 12:19 PM 
Nonlinear vectorial equation  FunWarrior  Linear Algebra  0  February 11th, 2014 01:22 AM 
Function Continuity  Tear_Grant  Calculus  2  April 19th, 2009 04:43 AM 