Trance-0/NoteNextra-origin
1
0
Fork 0
Code Issues Pull Requests Actions 1 Packages Projects Releases Wiki Activity

Update Math4121_L4.md

Browse Source
This commit is contained in:
Zheyuan Wu
2025-02-07 17:51:34 -06:00
parent b749de07c2
commit 7390326c4a
1 changed files with 4 additions and 2 deletions
Download Patch File Download Diff File Expand all files Collapse all files

6
pages/Math4121/Math4121_L4.md
View File

@@ -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 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(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)}\\ &=\lim_{x\to a}\frac{f(y)}{g(y)}\\
&=\frac{f'(y)}{g'(y)}\\ &=\frac{f'(y)}{g'(y)}\\
&\leq r<q &\leq r<q
\end{aligned}$$ \end{aligned}
$$
$\forall y\in (a,c)$, $\frac{f(y)}{g(y)}<q$. $\forall y\in (a,c)$, $\frac{f(y)}{g(y)}<q$.