Let $A=\{(x,y)\in \mathbb{R^2 }: x>0, 0 Let $f: \mathbb{R^2} \rightarrow \mathbb{R}$ be defined by $f(x)=0$ if $x$ is not in $A$ and $f(x)=1$ if $x\in A$. Show that $D_xf(0,0)$ exists for all $x$ although $f$ is not even continuous at $(0,0)$. Not sure how to tackle this one... Any hints will be appreciated. My attempt:
Show that $D_xf(0,0)$ exists for all $x$ although $f$ is not even continuous at $(0,0)$.
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real-analysis
analysis
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1Additionally to Thomas's hint have a look at the sequence $\left(\frac{1}{n^2}, \frac{1}{n}\right)_n$. – 2017-02-07
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0$D_xf(0,0)$ for all $x$ makes no sense. – 2017-02-07