Calculus: Other Calculus Problems – #28068

Question: (a) Show that the point (0, 0) is an accumulation point of \({{\mathbb{R}}^{2}}\backslash \left\{ \left( 0,y \right)|y\in \mathbb{R} \right\}\)

(b) Show using definition of limit that limit of a function \({{\mathbb{R}}^{2}}\backslash \left\{ \left( 0,y \right)|y\in \mathbb{R} \right\}\mapsto \mathbb{R}\)

\[f\left( x,y \right)=\frac{y}{x}\]

does not exist at (0, 0).

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