Update Math4121_L1.md

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2025-01-24 11:49:52 -06:00
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@@ -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