From baef7341913c8fb8ae02cd0812f230469f4ac436 Mon Sep 17 00:00:00 2001
From: unlockable <g@unlockableworld.com>
Date: Sun, 1 Jan 2023 20:13:56 +0800
Subject: [PATCH] =?UTF-8?q?=E6=94=B9=E9=94=99=E3=80=82?=
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---
 04微分与Taylor定理.tex | 4 ++--
 09常微分方程.tex       | 2 +-
 高等微积分.tex         | 2 +-
 3 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/04微分与Taylor定理.tex b/04微分与Taylor定理.tex
index 7cf9616..50d0249 100644
--- a/04微分与Taylor定理.tex
+++ b/04微分与Taylor定理.tex
@@ -253,6 +253,6 @@
 \end{proof}
 
 \begin{remark}
-    带Lagrange余项的Taylor公式也常常写作：设$f$在$(a,b)$内$n+1$阶可导，$\forall x_0, x \in (a,b)$，$\exists \xi$在$x_0$与$x$之间满足
-    \[f(x) = P_n(x - x_0) + \frac{f^{n+1}(x_0 + \theta \Delta x)}{(n+1)!}\Delta x^{n+1}\eqper\]
+    带Lagrange余项的Taylor公式也常常写作：设$f$在$(a,b)$内$n+1$阶可导，$\forall ~ x_0, x \in (a,b)$，$\exists ~ \xi$在$x_0$与$x$之间满足
+    \[f(x) = P_n(x - x_0) + \frac{f^{(n+1)}(\xi)}{(n+1)!}\Delta x^{n+1}\eqper\]
 \end{remark}
\ No newline at end of file
diff --git a/09常微分方程.tex b/09常微分方程.tex
index b84e17b..5740b3a 100644
--- a/09常微分方程.tex
+++ b/09常微分方程.tex
@@ -84,7 +84,7 @@
         y > 0\text{时，}y & = e^{C_1}e^{x^2}\\
         y < 0\text{时，}y & = -e^{C_1}e^{x^2}\\
         \intertext{记$C = \pm e^{C_1}$，则有}
-        y & = Ce^{x_2} (C \neq 0)
+        y & = Ce^{x^2} (C \neq 0)
     \end{align*}
     同时注意到$y \equiv 0$也是方程的解，在分离变量时被丢掉了。因此$C = 0$时也成立。因此方程的通解为
     \[y = Ce^{x^2} (C \in \realnum) \eqper \qedhere\]
diff --git a/高等微积分.tex b/高等微积分.tex
index de261dd..b50c6c3 100644
--- a/高等微积分.tex
+++ b/高等微积分.tex
@@ -61,7 +61,7 @@
 \date{}
 % linespread{1.5}
 
-\includeonly{09常微分方程.tex}
+% \includeonly{09常微分方程.tex}
 
 \begin{document}
     \maketitle