Update Math4121_L4.md

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Zheyuan Wu
2025-02-07 17:51:34 -06:00
parent b749de07c2
commit 7390326c4a

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@@ -90,12 +90,14 @@ Case 1: $f(x)\to 0$ and $g(x)\to 0$ as $x\to a$.
As $x\to a$, $f(x)\to 0$ and $g(x)\to 0$. So
$$\begin{aligned}
$$
\begin{aligned}
\lim_{x\to a}\frac{f(x)-f(y)}{g(x)-g(y)}&=\lim_{x\to a}\frac{0-f(y)}{0-g(y)}\\
&=\lim_{x\to a}\frac{f(y)}{g(y)}\\
&=\frac{f'(y)}{g'(y)}\\
&\leq r<q
\end{aligned}$$
\end{aligned}
$$
$\forall y\in (a,c)$, $\frac{f(y)}{g(y)}<q$.