From ed50b4643dbb8c669b5fdbd9331f534a98811c96 Mon Sep 17 00:00:00 2001
From: GitHub Action <action@github.com>
Date: Thu, 30 Nov 2023 08:59:57 +0000
Subject: [PATCH] Add changes for a57b23af22e1f33a5c71a715026b743bd5921671

---
 .doctrees/assets/notes/matematyka_cw.doctree  | Bin 4405 -> 17642 bytes
 .../matematyka_cw_2023.11.30.doctree          | Bin 0 -> 15047 bytes
 .doctrees/assets/notes/mechanika_cw.doctree   | Bin 4782 -> 4950 bytes
 .../mechanika_cw_24.11.2023.doctree           | Bin 3861 -> 4029 bytes
 .doctrees/environment.pickle                  | Bin 736536 -> 779891 bytes
 assets/notes/matematyka_cw.html               |  81 ++++++-
 .../matematyka_cw_2023.11.30.html             | 201 ++++++++++++++++++
 assets/notes/mechanika_cw.html                |   2 +-
 .../mechanika_cw/mechanika_cw_24.11.2023.html |   2 +-
 index.html                                    |   6 +-
 objects.inv                                   | Bin 895 -> 921 bytes
 searchindex.js                                |   2 +-
 12 files changed, 289 insertions(+), 5 deletions(-)
 create mode 100644 .doctrees/assets/notes/matematyka_cw/matematyka_cw_2023.11.30.doctree
 create mode 100644 assets/notes/matematyka_cw/matematyka_cw_2023.11.30.html

diff --git a/.doctrees/assets/notes/matematyka_cw.doctree b/.doctrees/assets/notes/matematyka_cw.doctree
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diff --git a/assets/notes/matematyka_cw.html b/assets/notes/matematyka_cw.html
index ad1d14ae..0cc0dcfd 100644
--- a/assets/notes/matematyka_cw.html
+++ b/assets/notes/matematyka_cw.html
@@ -82,6 +82,75 @@ <h1>Matematyka - ćwiczenia<a class="headerlink" href="#matematyka-cwiczenia" ti
 <p class="admonition-title">Wzór sterlinga</p>
 <p><span class="math notranslate nohighlight">\(n! = \sqrt{2\pi n} \left(\frac{n}{e}\right)^n\)</span></p>
 </div>
+<hr class="docutils" />
+<p><em>Notatki z pliku <code class="docutils literal notranslate"><span class="pre">notes/matematyka_cw/matematyka_cw_2023.11.30.md</span></code></em></p>
+<section id="przydatne-wlasnosci">
+<h2>Przydatne własności<a class="headerlink" href="#przydatne-wlasnosci" title="Link to this heading">¶</a></h2>
+<div class="admonition tip">
+<p class="admonition-title">Wskazówka</p>
+<p>Przy wistępowaniu nioznaconości typu <span class="math notranslate nohighlight">\([0 * \infty]\)</span> wystarczy iloczyn zapisać
+w postaci ilorazu na przykład</p>
+<div class="math notranslate nohighlight">
+\[
+\lim_{x \to 0} x * \left(\frac{1}{x}+1\right) = \frac{\frac{1}{x} + 1}{\frac{1}{x}}
+\]</div>
+<p>W ten sposób otrzymamy nieoznaczoność typu <span class="math notranslate nohighlight">\(\left[\frac{\infty}{\infty}\right]\)</span> więc możemy skorzystać z reguły
+de l’Hospital’a</p>
+</div>
+</section>
+<section id="przykladowa-tabela-przebiegu-zmiennosci-funkcji">
+<h2>Przykładowa tabela przebiegu zmienności funkcji:<a class="headerlink" href="#przykladowa-tabela-przebiegu-zmiennosci-funkcji" title="Link to this heading">¶</a></h2>
+<table class="docutils align-default">
+<thead>
+<tr class="row-odd"><th class="head"><p></p></th>
+<th class="head"><p><span class="math notranslate nohighlight">\((-\infty, -1)\)</span></p></th>
+<th class="head"><p><span class="math notranslate nohighlight">\(-1\)</span></p></th>
+<th class="head"><p><span class="math notranslate nohighlight">\(\left(-1, -\frac{2}{5} \right)\)</span></p></th>
+<th class="head"><p><span class="math notranslate nohighlight">\(-\frac{2}{5}\)</span></p></th>
+<th class="head"><p><span class="math notranslate nohighlight">\(\left(\frac{-2}{3}, 0\right)\)</span></p></th>
+<th class="head"><p>0</p></th>
+<th class="head"><p><span class="math notranslate nohighlight">\((0,2)\)</span></p></th>
+<th class="head"><p>2</p></th>
+<th class="head"><p><span class="math notranslate nohighlight">\((2, \infty)\)</span></p></th>
+</tr>
+</thead>
+<tbody>
+<tr class="row-even"><td><p><span class="math notranslate nohighlight">\(f'(x)\)</span></p></td>
+<td><p>+</p></td>
+<td><p>0</p></td>
+<td><p>-</p></td>
+<td><p>-</p></td>
+<td><p>-</p></td>
+<td><p>X</p></td>
+<td><p>-</p></td>
+<td><p>0</p></td>
+<td><p>+</p></td>
+</tr>
+<tr class="row-odd"><td><p><span class="math notranslate nohighlight">\(f''(x)\)</span></p></td>
+<td><p>-</p></td>
+<td><p>-</p></td>
+<td><p>-</p></td>
+<td><p>0</p></td>
+<td><p>+</p></td>
+<td><p>X</p></td>
+<td><p>+</p></td>
+<td><p>+</p></td>
+<td><p>+</p></td>
+</tr>
+<tr class="row-even"><td><p><span class="math notranslate nohighlight">\(f(x)\)</span></p></td>
+<td><p>rośnie</p></td>
+<td><p>max <span class="math notranslate nohighlight">\(e^{-1}\)</span></p></td>
+<td><p>maleje</p></td>
+<td><p>PP <span class="math notranslate nohighlight">\(\frac{8}{5}e^{-\frac{5}{2}}\)</span></p></td>
+<td><p>maleje</p></td>
+<td><p>X</p></td>
+<td><p>maleje</p></td>
+<td><p>min <span class="math notranslate nohighlight">\(4 \sqrt{e}\)</span></p></td>
+<td><p>rośnie</p></td>
+</tr>
+</tbody>
+</table>
+</section>
 </section>
 
 
@@ -90,7 +159,17 @@ <h1>Matematyka - ćwiczenia<a class="headerlink" href="#matematyka-cwiczenia" ti
         </div>
       </div>
       <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
-        <div class="sphinxsidebarwrapper">
+        <div class="sphinxsidebarwrapper"><div class="sphinx-toc sphinxlocaltoc">
+    <h3><a href="../../index.html">Spis treści:</a></h3>
+    <ul>
+<li><a class="reference internal" href="#">Matematyka - ćwiczenia</a><ul>
+<li><a class="reference internal" href="#przydatne-wlasnosci">Przydatne własności</a></li>
+<li><a class="reference internal" href="#przykladowa-tabela-przebiegu-zmiennosci-funkcji">Przykładowa tabela przebiegu zmienności funkcji:</a></li>
+</ul>
+</li>
+</ul>
+
+  </div>
   <div class="sphinxprev">
     <h4>Poprzednia strona</h4>
     <p class="topless"><a href="matematyka.html"
diff --git a/assets/notes/matematyka_cw/matematyka_cw_2023.11.30.html b/assets/notes/matematyka_cw/matematyka_cw_2023.11.30.html
new file mode 100644
index 00000000..6b0f56fd
--- /dev/null
+++ b/assets/notes/matematyka_cw/matematyka_cw_2023.11.30.html
@@ -0,0 +1,201 @@
+
+
+<!DOCTYPE html>
+
+<html lang="pl" data-content_root="../../../">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="viewport" content="width=device-width, initial-scale=1" />
+
+    <title>Przydatne własności &#8212; Matematyka  - dokumentacja</title>
+    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/cloud.css?v=f9ae72be" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/sphinxcontrib-images/LightBox2/lightbox2/dist/css/lightbox.css?v=5c84f910" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/css/custom.css?v=6897fae6" />
+    <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noticia+Text:400,i,b,bi|Open+Sans:400,i,b,bi|Roboto+Mono:400,i,b,bi&amp;display=swap" type="text/css" />
+    
+    <script src="../../../_static/documentation_options.js?v=a28d12eb"></script>
+    <script src="../../../_static/doctools.js?v=888ff710"></script>
+    <script src="../../../_static/sphinx_highlight.js?v=dc90522c"></script>
+    <script src="../../../_static/translations.js?v=a186e9ce"></script>
+    <script src="../../../_static/sphinxcontrib-images/LightBox2/lightbox2/dist/js/lightbox-plus-jquery.min.js?v=ffc8af2d"></script>
+    <script src="../../../_static/sphinxcontrib-images/LightBox2/lightbox2-customize/jquery-noconflict.js?v=12818e64"></script>
+    <script>window.MathJax = {"options": {"processHtmlClass": "tex2jax_process|mathjax_process|math|output_area"}}</script>
+    <script defer="defer" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
+
+    
+    
+     
+        <script src="../../../_static/jquery.cookie.js"></script>
+    
+
+    
+     
+        <script src="../../../_static/cloud.base.js"></script>
+    
+
+    
+     
+        <script src="../../../_static/cloud.js"></script>
+    
+
+    <link rel="index" title="Indeks" href="../../../genindex.html" />
+    <link rel="search" title="Szukaj" href="../../../search.html" /> 
+        <meta name="viewport" content="width=device-width, initial-scale=1">
+  </head><body>
+    <div class="relbar-top">
+        
+    <div class="related" role="navigation" aria-label="related navigation">
+      <h3>Nawigacja</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="../../../genindex.html" title="Indeks ogólny"
+             accesskey="I">indeks</a></li>
+    <li><a href="../../../index.html">Matematyka  - dokumentacja</a> &#187;</li>
+
+        <li class="nav-item nav-item-this"><a href="">Przydatne własności</a></li> 
+      </ul>
+    </div>
+    </div>
+  
+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+            
+  <section id="przydatne-wlasnosci">
+<h1>Przydatne własności<a class="headerlink" href="#przydatne-wlasnosci" title="Link to this heading">¶</a></h1>
+<div class="admonition tip">
+<p class="admonition-title">Wskazówka</p>
+<p>Przy wistępowaniu nioznaconości typu <span class="math notranslate nohighlight">\([0 * \infty]\)</span> wystarczy iloczyn zapisać
+w postaci ilorazu na przykład</p>
+<div class="math notranslate nohighlight">
+\[
+\lim_{x \to 0} x * \left(\frac{1}{x}+1\right) = \frac{\frac{1}{x} + 1}{\frac{1}{x}}
+\]</div>
+<p>W ten sposób otrzymamy nieoznaczoność typu <span class="math notranslate nohighlight">\(\left[\frac{\infty}{\infty}\right]\)</span> więc możemy skorzystać z reguły
+de l’Hospital’a</p>
+</div>
+</section>
+<section id="przykladowa-tabela-przebiegu-zmiennosci-funkcji">
+<h1>Przykładowa tabela przebiegu zmienności funkcji:<a class="headerlink" href="#przykladowa-tabela-przebiegu-zmiennosci-funkcji" title="Link to this heading">¶</a></h1>
+<table class="docutils align-default">
+<thead>
+<tr class="row-odd"><th class="head"><p></p></th>
+<th class="head"><p><span class="math notranslate nohighlight">\((-\infty, -1)\)</span></p></th>
+<th class="head"><p><span class="math notranslate nohighlight">\(-1\)</span></p></th>
+<th class="head"><p><span class="math notranslate nohighlight">\(\left(-1, -\frac{2}{5} \right)\)</span></p></th>
+<th class="head"><p><span class="math notranslate nohighlight">\(-\frac{2}{5}\)</span></p></th>
+<th class="head"><p><span class="math notranslate nohighlight">\(\left(\frac{-2}{3}, 0\right)\)</span></p></th>
+<th class="head"><p>0</p></th>
+<th class="head"><p><span class="math notranslate nohighlight">\((0,2)\)</span></p></th>
+<th class="head"><p>2</p></th>
+<th class="head"><p><span class="math notranslate nohighlight">\((2, \infty)\)</span></p></th>
+</tr>
+</thead>
+<tbody>
+<tr class="row-even"><td><p><span class="math notranslate nohighlight">\(f'(x)\)</span></p></td>
+<td><p>+</p></td>
+<td><p>0</p></td>
+<td><p>-</p></td>
+<td><p>-</p></td>
+<td><p>-</p></td>
+<td><p>X</p></td>
+<td><p>-</p></td>
+<td><p>0</p></td>
+<td><p>+</p></td>
+</tr>
+<tr class="row-odd"><td><p><span class="math notranslate nohighlight">\(f''(x)\)</span></p></td>
+<td><p>-</p></td>
+<td><p>-</p></td>
+<td><p>-</p></td>
+<td><p>0</p></td>
+<td><p>+</p></td>
+<td><p>X</p></td>
+<td><p>+</p></td>
+<td><p>+</p></td>
+<td><p>+</p></td>
+</tr>
+<tr class="row-even"><td><p><span class="math notranslate nohighlight">\(f(x)\)</span></p></td>
+<td><p>rośnie</p></td>
+<td><p>max <span class="math notranslate nohighlight">\(e^{-1}\)</span></p></td>
+<td><p>maleje</p></td>
+<td><p>PP <span class="math notranslate nohighlight">\(\frac{8}{5}e^{-\frac{5}{2}}\)</span></p></td>
+<td><p>maleje</p></td>
+<td><p>X</p></td>
+<td><p>maleje</p></td>
+<td><p>min <span class="math notranslate nohighlight">\(4 \sqrt{e}\)</span></p></td>
+<td><p>rośnie</p></td>
+</tr>
+</tbody>
+</table>
+</section>
+
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
+        <div class="sphinxsidebarwrapper"><div class="sphinx-toc sphinxlocaltoc">
+    <h3><a href="../../../index.html">Spis treści:</a></h3>
+    <ul>
+<li><a class="reference internal" href="#">Przydatne własności</a></li>
+<li><a class="reference internal" href="#przykladowa-tabela-przebiegu-zmiennosci-funkcji">Przykładowa tabela przebiegu zmienności funkcji:</a></li>
+</ul>
+
+  </div>
+<div id="searchbox" style="display: none" role="search">
+  <h3 id="searchlabel">Szybkie wyszukiwanie</h3>
+    <div class="searchformwrapper">
+    <form class="search" action="../../../search.html" method="get">
+      <input type="text" name="q" aria-labelledby="searchlabel" autocomplete="off" autocorrect="off" autocapitalize="off" spellcheck="false"/>
+      <input type="submit" value="Szukaj" />
+    </form>
+    </div>
+</div>
+<script>document.getElementById('searchbox').style.display = "block"</script>
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+    
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+        <div class="sidebar-toggle-group no-js">
+            
+            <button class="sidebar-toggle" id="sidebar-hide" title="Hide the sidebar menu">
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+                
+                <span class="show-for-small">menu</span>
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+                 »
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+        </div>
+    
+      <div class="clearer"></div>
+    </div>
+    <div class="relbar-bottom">
+        
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+      <h3>Nawigacja</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="../../../genindex.html" title="Indeks ogólny"
+             >indeks</a></li>
+    <li><a href="../../../index.html">Matematyka  - dokumentacja</a> &#187;</li>
+
+        <li class="nav-item nav-item-this"><a href="">Przydatne własności</a></li> 
+      </ul>
+    </div>
+    </div>
+
+    <div class="footer" role="contentinfo">
+    &#169; Copyright 2023, Maciej Sz.
+      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 7.2.6.
+    </div>
+    <!-- cloud_sptheme 1.4 -->
+  </body>
+</html>
\ No newline at end of file
diff --git a/assets/notes/mechanika_cw.html b/assets/notes/mechanika_cw.html
index 9b747349..1ff8b2fe 100644
--- a/assets/notes/mechanika_cw.html
+++ b/assets/notes/mechanika_cw.html
@@ -80,7 +80,7 @@ <h1>Mechanika - Ćwiczenia<a class="headerlink" href="#mechanika-cwiczenia" titl
 <div class="math notranslate nohighlight">
 \[
 grad F(x, y, z) = \vec{A}(x,y,z)
-(\frac{d}{dx}, \frac{d}{dy}, \frac{d}{dz})
+\left(\frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z}\right)
 \]</div>
 </div>
 </section>
diff --git a/assets/notes/mechanika_cw/mechanika_cw_24.11.2023.html b/assets/notes/mechanika_cw/mechanika_cw_24.11.2023.html
index 55bf0877..9046c3ee 100644
--- a/assets/notes/mechanika_cw/mechanika_cw_24.11.2023.html
+++ b/assets/notes/mechanika_cw/mechanika_cw_24.11.2023.html
@@ -72,7 +72,7 @@ <h1>Mechanika - Ćwiczenia<a class="headerlink" href="#mechanika-cwiczenia" titl
 <div class="math notranslate nohighlight">
 \[
 grad F(x, y, z) = \vec{A}(x,y,z)
-(\frac{d}{dx}, \frac{d}{dy}, \frac{d}{dz})
+\left(\frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z}\right)
 \]</div>
 </div>
 </section>
diff --git a/index.html b/index.html
index 9fd3b546..81865d7e 100644
--- a/index.html
+++ b/index.html
@@ -154,7 +154,11 @@ <h1>Wstęp<a class="headerlink" href="#wstep" title="Link to this heading">¶</a
 </div>
 <div class="toctree-wrapper compound">
 <ul>
-<li class="toctree-l1"><a class="reference internal" href="assets/notes/matematyka_cw.html">Matematyka - ćwiczenia</a></li>
+<li class="toctree-l1"><a class="reference internal" href="assets/notes/matematyka_cw.html">Matematyka - ćwiczenia</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="assets/notes/matematyka_cw.html#przydatne-wlasnosci">Przydatne własności</a></li>
+<li class="toctree-l2"><a class="reference internal" href="assets/notes/matematyka_cw.html#przykladowa-tabela-przebiegu-zmiennosci-funkcji">Przykładowa tabela przebiegu zmienności funkcji:</a></li>
+</ul>
+</li>
 </ul>
 </div>
 <div class="toctree-wrapper compound">
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