diff --git a/pages/Math4121/Math4121_L1.md b/pages/Math4121/Math4121_L1.md index 75f1071..86ca7e1 100644 --- a/pages/Math4121/Math4121_L1.md +++ b/pages/Math4121/Math4121_L1.md @@ -28,6 +28,12 @@ Let $f:[a,b]\to \mathbb{R}$. If $f$ is differentiable at $x\in [a,b]$, then $f$ Proof: +> Recall [Definition 4.5](https://notenextra.trance-0.com/Math4111/Math4111_L22#definition-45) +> +> $f$ is continuous at $x$ if $\forall \epsilon > 0, \exists \delta > 0$ such that if $|t-x| < \delta$, then $|f(t)-f(x)| < \epsilon$. +> +> Whenever you see a limit, you should think of this definition. + We need to show that $\lim_{t\to x} f(t) = f(x)$. Equivalently, we need to show that