Functions of Several Variables

Limit and Continuity of Functions with Several Variables

Limit

Definition

Let $f:R^n\mapsto R$ where $D=dom(f)\subseteq R^n$, $p\in D$. We say that limit of f at $p_0$ is $L\in R$. We say that limit of f at $p_0$ is $L\in R$ and we write

$li{m}_{p\to p_0}f(p)=L$

if $\forall ϵ>0,\exists \sigma >0$ st. $0<|p-p_0|<\sigma ⟹|f(p)-L|<ϵ$.

Remember that if $h(X)$ is cont. then $li{m}_{p\to p_0}h(p)=h(li{m}_{p\to p_0})$

Warning

L’H is NOT applicable for two variable functions.

Todo

• Examples and exercises in Week 3 Note 2

Continuity