From 7390326c4ab4f1d467702d9b12f67cc32ea32d61 Mon Sep 17 00:00:00 2001 From: Zheyuan Wu <60459821+Trance-0@users.noreply.github.com> Date: Fri, 7 Feb 2025 17:51:34 -0600 Subject: [PATCH] Update Math4121_L4.md --- pages/Math4121/Math4121_L4.md | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/pages/Math4121/Math4121_L4.md b/pages/Math4121/Math4121_L4.md index b6cfb4f..842e727 100644 --- a/pages/Math4121/Math4121_L4.md +++ b/pages/Math4121/Math4121_L4.md @@ -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