Differentiable and Continuous
Function f(x)가 x=a에서 미분 가능하면: p
f(x)는 연속이다. : q
(▲ implication, 조건명제)
- p⟹q 는 참(True)이나
- 이의 역(inverse)인 q⟹p는 거짓(False)임.

Example
- f(x)=|x| : x=0에서 continuous하지만 미분가능하지 않음.
2023.06.22 - [.../Math] - [Math] Continuity (of Multivariate Function) and Contiguity
[Math] Continuity (of Multivariate Function) and Contiguity
Continuity (연속) 이란 If S⊆Rn, then a function f:S→R is continuous at a∈S if $$\begin{equation}\label{cont.def} \forall \varepsilon >0, \ \ \exists \delta>0 \mbox{ such that if } \mathbf x \in S \mbox{
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Differentiable의 조건 (Scalar Function)
- Function(함수)가 Continuous(연속)이어야 함.
- 만약 continuous(연속)이라면 좌미분계수 와 우미분계수가 같아야 함.
limx→a−f(x)−f(a)x−a=limx→a+f(x)−f(a)x−alimΔx→0−f(a+Δx)Δx=limΔx→0+f(a+Δx)Δxleft derivative=right derivative
더 읽어보면 좋은 자료
2023.06.23 - [.../Math] - [Math] Differentiability of MultivariableFunctions
[Math] Differentiability of MultivariableFunctions
Differentiability f:Rn→Rm 이고, a∈Rn이면서 f의 domain에 속한다고 하자. 이 때 $$ \underset{\textbf{x}\to\textbf{a}}{\lim} \frac{\textbf{f}(\textbf{x})-\textbf{f}(\textbf{a
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https://dsaint31.github.io/math/math-week03/
[Math] Week 03
Limit and Continuity
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