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cyrxdzj committed Oct 11, 2023
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2 changes: 1 addition & 1 deletion 2021-07-02-LuoguMonthlyCompetition202105Summary/index.html
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&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
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2 changes: 1 addition & 1 deletion 2021-07-07-HowToUseLuoguCard/index.html
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&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
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2 changes: 1 addition & 1 deletion 2021-07-09-Grade7Term2FinalExamSummary/index.html
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Expand Up @@ -882,7 +882,7 @@ <h3 id="十、总分与排名"><a href="#十、总分与排名" class="headerlin
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&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">15.3k</span>&nbsp;字
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2 changes: 1 addition & 1 deletion 2021-07-09-Grade7Term2MidtermExamSummary/index.html
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&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">15.3k</span>&nbsp;字
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2 changes: 1 addition & 1 deletion 2021-07-22-LuoguMonthlyCompetition202107Summary/index.html
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Expand Up @@ -1189,7 +1189,7 @@ <h3 id="五、总分"><a href="#五、总分" class="headerlink" title="五、
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&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">15.3k</span>&nbsp;字
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2 changes: 1 addition & 1 deletion 2023-05-21-TalkingAboutComputerSecurityFromTheIntelligentClassromSystem/index.html
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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
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&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">15.3k</span>&nbsp;字
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2 changes: 1 addition & 1 deletion 2023-09-22-CyrxNote-Math-001/index.html
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&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
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2 changes: 1 addition & 1 deletion 2023-09-22-CyrxNoteIndex/index.html
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Expand Up @@ -882,7 +882,7 @@ <h1 class="description center-align post-title">cyrxdzj的文化课学习笔记
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&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">15.3k</span>&nbsp;字
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2 changes: 1 addition & 1 deletion 2023-09-23-CyrxNote-Math-002/index.html
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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
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2 changes: 1 addition & 1 deletion 2023-09-28-CyrxNote-Chemistry-001/index.html
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Expand Up @@ -1008,7 +1008,7 @@ <h3 id="花絮"><a href="#花絮" class="headerlink" title="花絮"></a>花絮</
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&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">15.3k</span>&nbsp;字
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2 changes: 1 addition & 1 deletion 2023-10-04-CyrxNote-Math-003/index.html
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Expand Up @@ -1036,7 +1036,7 @@ <h3 id="9、尝试将其它字母分离出来"><a href="#9、尝试将其它字
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&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">15.3k</span>&nbsp;字
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23 changes: 21 additions & 2 deletions 2023-10-09-CyrxNote-Math-004/index.html
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Expand Up @@ -454,7 +454,7 @@ <h1 class="description center-align post-title">cyrxdzj的文化课学习笔记

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<i class="far fa-file-word fa-fw"></i>文章字数:&nbsp;&nbsp;
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Expand Down Expand Up @@ -602,6 +602,25 @@ <h3 id="5、分段函数之对齐分段"><a href="#5、分段函数之对齐分
<p>我们可以发现函数完完全全就是 $f(x)=x$ 诶。函数图象如下：</p>
<p><img src="../post_image/CyrxNote-Math-004/CyrxNote-Math-004-05.PNG" alt=""></p>
<p>上图中，红色线和绿色线是拆分后的函数，紫色线是合并后要求的函数。函数与颜色的对应关系在左边有写。</p>
<h3 id="5、找规律"><a href="#5、找规律" class="headerlink" title="5、找规律"></a>5、找规律</h3><p>已知分段函数 $f(x)=\left\lbrace\begin{matrix}x^2, &amp;x&lt;1, \\f(x-1)-1, &amp;x\ge1,\end{matrix}\right.$，求以下函数的值：</p>
<ol>
<li><p>$f(2)$</p>
</li>
<li><p>$f(2023)$</p>
</li>
<li><p>$f(2023.6)$</p>
</li>
<li><p>$f(-0.6)$</p>
</li>
</ol>
<p>对于第 1 题，可以爆算，$f(2)=f(1)-1=f(0)-1-1=0^2-1-1=-2$。</p>
<p>对于第 2 题，显然不能爆算了，但是我们可以根据上一题找到规律，可以发现 $f(2023)=f(2022)-1=f(2021)-1-1=\dots =f(0)-2023\times1=-2023$，每计算一层，$f$ 中的参数都会减 $1$，同时式子后面就会多个 $-1$。</p>
<p>对于第 3 题，可以发现 $f(2023.6)=f(2022.6)-1=f(2021.6)-1-1=\dots =f(0.6)-2023\times1=0.6^2-2023=-2022.64$。有点难，但细心分析应该不会有太大问题。</p>
<p>对于第 4 题，一上来就有 $x&lt;1$，所以 $f(-0.6)=(-0.6)^2=0.36$。</p>
<p>经计算机验证，这是正确的：</p>
<p><img src="../post_image/CyrxNote-Math-004/CyrxNote-Math-004-06.PNG" alt=""></p>
<p>当然考试时没有计算机的。</p>
<p>对于这类问题，可以稍微爆算几轮，发现规律，同时根据函数解析式验证规律。</p>


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Expand Down Expand Up @@ -976,7 +995,7 @@ <h3 id="5、分段函数之对齐分段"><a href="#5、分段函数之对齐分
<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">15.3k</span>&nbsp;字
class="white-color">15.6k</span>&nbsp;字



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2 changes: 1 addition & 1 deletion 404/index.html
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<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">15.3k</span>&nbsp;字
class="white-color">15.6k</span>&nbsp;字



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2 changes: 1 addition & 1 deletion about/index.html
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<br>

&nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
class="white-color">15.3k</span>&nbsp;字
class="white-color">15.6k</span>&nbsp;字



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