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 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 Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post MathAboveMeth Calculus 1 January 7th, 2017 03:55 AM juanpe966 Calculus 4 February 27th, 2016 02:24 PM condemath2 Calculus 6 June 6th, 2014 12:19 PM FunWarrior Linear Algebra 0 February 11th, 2014 01:22 AM Tear_Grant Calculus 2 April 19th, 2009 04:43 AM

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