Continuity

[Math] Continuous 와 Differentiable 의 관계

Differentiable and ContinuousFunction $f(x)$가 $x=a$에서 미분 가능 ($p$) 하면 $f(x)$는 연속이다($q$). (← implication, 조건명제)$p \implies q$ 는 참(True)이나 이의 역인 $q \implies p$는 거짓(False)임.Example$f(x)=|x|$ : $x=0$에서 continuous하지만 미분가능하지 않음.2023.06.22 - [.../Math] - [Math] Continuity (of Multivariate Function) and Contiguity0, \ \ \exists \delta>0 \mbox{ such that if } \mathbf x \in S \mbox{" data-og-host="dsaint31..

[Math] Continuity (of Multivariate Function) and Contiguity

Continuity (연속) 이란 If $S\subseteq \mathbb{R}^n$, then a function $f:S\to \mathbb{R}$ is continuous at $\textbf{a} \in S$ if $$\begin{equation}\label{cont.def} \forall \varepsilon >0, \ \ \exists \delta>0 \mbox{ such that if } \mathbf x \in S \mbox{ and } |\mathbf x - \mathbf a| 1.2: Limits and Continuity Our goal is to show that \[\begin{equation}\label{facta} \forall \varepsilon >0, \exists\del..