Originally Posted by

**freya81** 1. a) If f is a real-valued function defined throughout R², except at the origin (0, 0), define what is meant by the statement: f (x, y)→ L as (x, y)→ (0, 0).

This is just book-work, you should be able to just look it

up in any text book or your notes.

$\displaystyle \ f (\bold{x})\ \rightarrow\ L\ as\ \bold{x}\ \rightarrow\ 0\ $

means that for all $\displaystyle \varepsilon\ >\ 0$ there exists $\displaystyle \delta\ >\ 0$ such that

$\displaystyle \|\bold{x}\|<\delta\ \Rightarrow\ \|f(\bold{x})-L\|\ <\ \varepsilon$

where $\displaystyle \|\cdot\|$ in its first occurrence above is the 2-vector

norm,and in its second occurrence is the absolute value, that is they

denote the appropriate norms for the domain and range of $\displaystyle f$

respectivly.

RonL