Skip to content

Commit

Permalink
Site updated: 2023-10-09 21:10:27
Browse files Browse the repository at this point in the history
  • Loading branch information
@cyrxdzj
cyrxdzj committed Oct 9, 2023
1 parent 781bed6 commit fe04675
Show file tree
Hide file tree
Showing 37 changed files with 72 additions and 44 deletions.
2 changes: 1 addition & 1 deletion 2021-07-02-LuoguMonthlyCompetition202105Summary/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -1065,7 +1065,7 @@ <h3 id="六、后记"><a href="#六、后记" class="headerlink" title="六、
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
2 changes: 1 addition & 1 deletion 2021-07-07-HowToUseLuoguCard/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -923,7 +923,7 @@ <h2 id="镜像仓库"><a href="#镜像仓库" class="headerlink" title="镜像
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
2 changes: 1 addition & 1 deletion 2021-07-09-Grade7Term2FinalExamSummary/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -882,7 +882,7 @@ <h3 id="十、总分与排名"><a href="#十、总分与排名" class="headerlin
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
2 changes: 1 addition & 1 deletion 2021-07-09-Grade7Term2MidtermExamSummary/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -867,7 +867,7 @@ <h3 id="十、后记"><a href="#十、后记" class="headerlink" title="十、
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
2 changes: 1 addition & 1 deletion 2021-07-22-LuoguMonthlyCompetition202107Summary/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -1189,7 +1189,7 @@ <h3 id="五、总分"><a href="#五、总分" class="headerlink" title="五、
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
2 changes: 1 addition & 1 deletion 2023-05-21-TalkingAboutComputerSecurityFromTheIntelligentClassromSystem/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -858,7 +858,7 @@ <h3 id="解决问题的建议"><a href="#解决问题的建议" class="headerlin
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
2 changes: 1 addition & 1 deletion 2023-09-22-CyrxNote-Math-001/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -919,7 +919,7 @@ <h3 id="链接阅读"><a href="#链接阅读" class="headerlink" title="链接
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
2 changes: 1 addition & 1 deletion 2023-09-23-CyrxNote-Math-002/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -915,7 +915,7 @@ <h3 id="5、当集合的内容为不等式解集时，集合间的关系"><a hre
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
2 changes: 1 addition & 1 deletion 2023-09-28-CyrxNote-Chemistry-001/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -1008,7 +1008,7 @@ <h3 id="花絮"><a href="#花絮" class="headerlink" title="花絮"></a>花絮</
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
2 changes: 1 addition & 1 deletion 2023-10-04-CyrxNote-Math-003/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -1035,7 +1035,7 @@ <h3 id="9、尝试将其它字母分离出来"><a href="#9、尝试将其它字
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
32 changes: 30 additions & 2 deletions 2023-10-09-CyrxNote-Math-004/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -454,7 +454,7 @@ <h1 class="description center-align post-title">cyrxdzj的文化课学习笔记

<div class="info-break-policy">
<i class="far fa-file-word fa-fw"></i>文章字数:&nbsp;&nbsp;
719
1.4k
</div>


Expand Down Expand Up @@ -498,6 +498,34 @@ <h3 id="2、与一元二次函数结合起来"><a href="#2、与一元二次函
<p><img src="../post_image/CyrxNote-Math-004/CyrxNote-Math-004-01.PNG" alt=""></p>
<p>可以计算得出，当 $x=0$ 时，函数值为 $0$。当 $x=2$ 时，函数值取到最小值，为 $-4$。当 $x=4$ 时，函数值再次为 $0$。</p>
<p>因此，可以得出 $2\le m\le4$。如果 $m$ 太小，函数值就不够小；如果 $m$ 太大，函数值就会超过 $0$。</p>
<h3 id="3、当给出的函数不标准的时候"><a href="#3、当给出的函数不标准的时候" class="headerlink" title="3、当给出的函数不标准的时候"></a>3、当给出的函数不标准的时候</h3><p>有些问题给出的函数，不会给 $f(x)$ 这种标准的形式，而是各种各样乱七八糟的形式。</p>
<p>已知 $f(2x-1)=4x^2$，则下列结论中正确的是：</p>
<p>A. $f(3)=-9$</p>
<p>B. $f(-3)=-4$</p>
<p>C. $f(x)=x^2$</p>
<p>D. $f(x)=(x+1)^2$</p>
<p>对于这类问题，首先为了避免混淆，先将题干中给出的函数变量改个名字，变成 $f(2a-1)=4a^2$。</p>
<p>然后，对于每个选项，挨个儿解出函数括号内的数对应的 $a$ 是多少。</p>
<p>例如，A 选项，我们可得 $2a-1=3$，解得 $a=2,4a^2=16\neq-9$。A 选项错误。</p>
<p>B 选项，我们可得 $2a-1=-3$，解得 $a=-1,4a^2=4\neq-4$，B 选项错误。</p>
<p>C 和 D 选项，我们可得 $2a-1=x$，稍稍细心计算，得 $a=\frac{x+1}{2}$，由此可得 $4a^2=(x+1)^2$，D 选项正确而 C 选项错误。</p>
<p>对于此类问题，应将题干中给出的原函数传入的参数（即 $2a-1$）和选项中给出的待验证函数传入的参数（即 $3$、$-3$、$x$）进行比对，要求两者相等，得出原函数传入的参数中的字母具体是什么（即，当 $2a-1=3$ 时 $a=2$），然后将字母代入计算。为避免混淆，可以将原函数中的字母统一更名。</p>
<h3 id="4、仔细分析更复杂的函数"><a href="#4、仔细分析更复杂的函数" class="headerlink" title="4、仔细分析更复杂的函数"></a>4、仔细分析更复杂的函数</h3><p>设 $f(x)=\frac{1+x^2}{1-x^2}$，则下列结论正确的是？请注意本题多选。</p>
<p>A. $f(-x)=-f(x)$</p>
<p>B. $f(\frac{1}{x})=-f(x)$</p>
<p>C. $f(-\frac{1}{x})=f(x)$</p>
<p>D. $f(-x)=f(x)$</p>
<p>我们可以发现，$x^2=(-x)^2$，$x$ 的正负性并不影响平方的结果。因此，$\frac{1+x^2}{1-x^2}=\frac{1+(-x)^2}{1-(-x)^2}$，由此可得 $f(-x)=f(x)$，A 选项错误，D 选项正确。</p>
<p>顺便说一句，这样的函数叫做<strong>偶函数</strong>，函数关于 $y$ 轴<strong>对称</strong>，图象如下：</p>
<p><img src="../post_image/CyrxNote-Math-004/CyrxNote-Math-004-02.PNG" alt=""></p>
<p>同时，我们可以得到 $f(\frac{1}{x})=f(-\frac{1}{x})$，这一条待会有用。</p>
<p>接下来，细心推出以下式子：</p>
<p>$f(\frac{1}{x})\\=\frac{1+\frac{1}{x}^2}{1-\frac{1}{x}^2}\\=\frac{x^2+1}{x^2}\div\frac{x^2-1}{x^2}\\=\frac{1+x^2}{x^2-1}$</p>
<p>至此，函数 $f(\frac{1}{x})$ 计算完毕。</p>
<p>而函数 $f(x)=\frac{1+x^2}{1-x^2}$，可以很容易地发现 $f(\frac{1}{x})=-f(x)$，B 选项正确，C 选项错误。图象如下：</p>
<p><img src="../post_image/CyrxNote-Math-004/CyrxNote-Math-004-03.PNG" alt=""></p>
<p>可以恰好发现 $f(x)$ 与 $f(\frac{1}{x})$ 关于 $x$ 轴对称。</p>
<p>对于此类问题，应细心审题，谨慎作答，答后验证。</p>


</div>
Expand Down Expand Up @@ -870,7 +898,7 @@ <h3 id="2、与一元二次函数结合起来"><a href="#2、与一元二次函
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
4 changes: 2 additions & 2 deletions 2023-10-09-CyrxNoteIndex/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -508,7 +508,7 @@ <h1 class="description center-align post-title">cyrxdzj的文化课学习笔记
<td>数学</td>
<td><a href="/2023-10-09-CyrxNote-Math-004/">cyrxdzj的文化课学习笔记 数学004 函数</a></td>
<td>2023-10-09 07:01:12</td>
<td>2023-10-09 18:48:51</td>
<td>2023-10-09 21:08:29</td>
</tr>
<tr>
<td>化学</td>
Expand Down Expand Up @@ -884,7 +884,7 @@ <h1 class="description center-align post-title">cyrxdzj的文化课学习笔记
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
2 changes: 1 addition & 1 deletion 404/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -344,7 +344,7 @@
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
2 changes: 1 addition & 1 deletion about/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -801,7 +801,7 @@
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
2 changes: 1 addition & 1 deletion archives/2021/07/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -738,7 +738,7 @@
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
2 changes: 1 addition & 1 deletion archives/2021/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -738,7 +738,7 @@
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
2 changes: 1 addition & 1 deletion archives/2023/05/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -518,7 +518,7 @@
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
2 changes: 1 addition & 1 deletion archives/2023/09/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -632,7 +632,7 @@
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
2 changes: 1 addition & 1 deletion archives/2023/10/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -642,7 +642,7 @@
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
2 changes: 1 addition & 1 deletion archives/2023/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -876,7 +876,7 @@
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
2 changes: 1 addition & 1 deletion archives/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -1161,7 +1161,7 @@
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
8 changes: 4 additions & 4 deletions atom.xml
View file
Original file line number Diff line number Diff line change
Expand Up @@ -6,7 +6,7 @@
<link href="https://blog.cyrxdzj.eu.org/atom.xml" rel="self"/>

<link href="https://blog.cyrxdzj.eu.org/"/>
<updated>2023-10-09T10:50:51.009Z</updated>
<updated>2023-10-09T13:08:54.594Z</updated>
<id>https://blog.cyrxdzj.eu.org/</id>

<author>
Expand All @@ -20,8 +20,8 @@
<title>cyrxdzj的文化课学习笔记 目录</title>
<link href="https://blog.cyrxdzj.eu.org/2023-10-09-CyrxNoteIndex/"/>
<id>https://blog.cyrxdzj.eu.org/2023-10-09-CyrxNoteIndex/</id>
<published>2023-10-09T10:50:51.000Z</published>
<updated>2023-10-09T10:50:51.009Z</updated>
<published>2023-10-09T13:08:54.000Z</published>
<updated>2023-10-09T13:08:54.594Z</updated>



Expand All @@ -45,7 +45,7 @@
<link href="https://blog.cyrxdzj.eu.org/2023-10-09-CyrxNote-Math-004/"/>
<id>https://blog.cyrxdzj.eu.org/2023-10-09-CyrxNote-Math-004/</id>
<published>2023-10-08T23:01:12.000Z</published>
<updated>2023-10-09T10:50:45.993Z</updated>
<updated>2023-10-09T13:09:35.132Z</updated>



Expand Down
4 changes: 2 additions & 2 deletions baidusitemap.xml
View file
Original file line number Diff line number Diff line change
@@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
<urlset xmlns="http://www.sitemaps.org/schemas/sitemap/0.9">
<url>
<loc>https://blog.cyrxdzj.eu.org/2023-10-04-CyrxNote-Math-003/</loc>
<loc>https://blog.cyrxdzj.eu.org/2023-10-09-CyrxNote-Math-004/</loc>
<lastmod>2023-10-09</lastmod>
</url>
<url>
<loc>https://blog.cyrxdzj.eu.org/2023-10-09-CyrxNoteIndex/</loc>
<lastmod>2023-10-09</lastmod>
</url>
<url>
<loc>https://blog.cyrxdzj.eu.org/2023-10-09-CyrxNote-Math-004/</loc>
<loc>https://blog.cyrxdzj.eu.org/2023-10-04-CyrxNote-Math-003/</loc>
<lastmod>2023-10-09</lastmod>
</url>
<url>
Expand Down
2 changes: 1 addition & 1 deletion categories/cyrxdzj的文化课学习笔记/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -689,7 +689,7 @@
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
2 changes: 1 addition & 1 deletion categories/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -481,7 +481,7 @@
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
2 changes: 1 addition & 1 deletion categories/一些杂七杂八的东西/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -471,7 +471,7 @@
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
2 changes: 1 addition & 1 deletion categories/学校生活/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -511,7 +511,7 @@
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
2 changes: 1 addition & 1 deletion categories/杂谈/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -471,7 +471,7 @@
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
2 changes: 1 addition & 1 deletion categories/比赛总结/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -511,7 +511,7 @@
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
2 changes: 1 addition & 1 deletion friends/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -650,7 +650,7 @@ <h1 class="friend-name">dengziyue</h1>
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
2 changes: 1 addition & 1 deletion index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -1160,7 +1160,7 @@ <h3 class="post-title">如何使用luogu-card</h3>
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">14k</span>&nbsp;字
class="white-color">14.6k</span>&nbsp;字



Expand Down
Binary file added post_image/CyrxNote-Math-004/CyrxNote-Math-004-02.PNG
View file
Loading
Sorry, something went wrong. Reload?
Sorry, we cannot display this file.
Sorry, this file is invalid so it cannot be displayed.
Binary file added post_image/CyrxNote-Math-004/CyrxNote-Math-004-03.PNG
View file
Loading
Sorry, something went wrong. Reload?
Sorry, we cannot display this file.
Sorry, this file is invalid so it cannot be displayed.
Loading

1 comment on commit fe04675

@vercel
Copy link

@vercel vercel bot commented on fe04675 Oct 9, 2023

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Successfully deployed to the following URLs:

cyrxdzj-github-io – ./

cyrxdzj-github-io-git-master-cyrxdzj.vercel.app
cyrxdzj-github-io.vercel.app
blog.cyrxdzj.eu.org
cyrxdzj-github-io-cyrxdzj.vercel.app

Please sign in to comment.