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	<id>http://brain.fuw.edu.pl/edu/index.php?action=history&amp;feed=atom&amp;title=Matematyka_1NI%2FCi%C4%85g%C5%82o%C5%9B%C4%87_zwyk%C5%82a</id>
	<title>Matematyka 1NI/Ciągłość zwykła - Historia wersji</title>
	<link rel="self" type="application/atom+xml" href="http://brain.fuw.edu.pl/edu/index.php?action=history&amp;feed=atom&amp;title=Matematyka_1NI%2FCi%C4%85g%C5%82o%C5%9B%C4%87_zwyk%C5%82a"/>
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	<updated>2026-04-25T17:59:42Z</updated>
	<subtitle>Historia wersji tej strony wiki</subtitle>
	<generator>MediaWiki 1.34.1</generator>
	<entry>
		<id>http://brain.fuw.edu.pl/edu/index.php?title=Matematyka_1NI/Ci%C4%85g%C5%82o%C5%9B%C4%87_zwyk%C5%82a&amp;diff=2921&amp;oldid=prev</id>
		<title>Anula o 15:04, 26 maj 2015</title>
		<link rel="alternate" type="text/html" href="http://brain.fuw.edu.pl/edu/index.php?title=Matematyka_1NI/Ci%C4%85g%C5%82o%C5%9B%C4%87_zwyk%C5%82a&amp;diff=2921&amp;oldid=prev"/>
		<updated>2015-05-26T15:04:15Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;pl&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← poprzednia wersja&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Wersja z 15:04, 26 maj 2015&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l292&quot; &gt;Linia 292:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 292:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;0\leq \left|\cos\frac{1}{x}-\cos\frac{1}{x_0}\right|&amp;lt;\frac{|x_0-x|}{\frac{1}{2}x_0^2}&amp;lt;\frac{2\delta}{x_0^2}\; .\,&amp;lt;/math&amp;gt;&amp;lt;/equation&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;0\leq \left|\cos\frac{1}{x}-\cos\frac{1}{x_0}\right|&amp;lt;\frac{|x_0-x|}{\frac{1}{2}x_0^2}&amp;lt;\frac{2\delta}{x_0^2}\; .\,&amp;lt;/math&amp;gt;&amp;lt;/equation&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Biorąc teraz&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Biorąc teraz&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;equation&amp;gt;  &lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;equation &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;id=&amp;quot;eq:eq2&amp;quot;&lt;/ins&gt;&amp;gt;  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;\delta=\frac{x_0^2}{2}\, \epsilon\; ,\,&amp;lt;/math&amp;gt;&amp;lt;/equation&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;\delta=\frac{x_0^2}{2}\, \epsilon\; ,\,&amp;lt;/math&amp;gt;&amp;lt;/equation&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;otrzymujemy:&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;otrzymujemy:&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Anula</name></author>
		
	</entry>
	<entry>
		<id>http://brain.fuw.edu.pl/edu/index.php?title=Matematyka_1NI/Ci%C4%85g%C5%82o%C5%9B%C4%87_zwyk%C5%82a&amp;diff=2920&amp;oldid=prev</id>
		<title>Anula o 15:03, 26 maj 2015</title>
		<link rel="alternate" type="text/html" href="http://brain.fuw.edu.pl/edu/index.php?title=Matematyka_1NI/Ci%C4%85g%C5%82o%C5%9B%C4%87_zwyk%C5%82a&amp;diff=2920&amp;oldid=prev"/>
		<updated>2015-05-26T15:03:16Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;pl&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← poprzednia wersja&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Wersja z 15:03, 26 maj 2015&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l234&quot; &gt;Linia 234:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 234:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;\, &amp;lt;/math&amp;gt;&amp;lt;/equation&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;\, &amp;lt;/math&amp;gt;&amp;lt;/equation&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Biorąc teraz  &lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Biorąc teraz  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;equation&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;equation &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;id=&amp;quot;eq:eq1&amp;quot;&lt;/ins&gt;&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;\delta=\frac{x_0^{\frac{k-1}{k}}}{2(1-\sqrt[k]{\frac{1}{2}})}\,\epsilon\; ,&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;\delta=\frac{x_0^{\frac{k-1}{k}}}{2(1-\sqrt[k]{\frac{1}{2}})}\,\epsilon\; ,&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;\, &amp;lt;/math&amp;gt;&amp;lt;/equation&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;\, &amp;lt;/math&amp;gt;&amp;lt;/equation&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Anula</name></author>
		
	</entry>
	<entry>
		<id>http://brain.fuw.edu.pl/edu/index.php?title=Matematyka_1NI/Ci%C4%85g%C5%82o%C5%9B%C4%87_zwyk%C5%82a&amp;diff=1205&amp;oldid=prev</id>
		<title>Anula: Utworzono nową stronę &quot;==Ciągłość zwykła==  &lt;big&gt;'''''Zadanie 1'''''&lt;/big&gt;  Wykazać ciągłość funkcji &lt;math&gt;f(x)=\cos x\, &lt;/math&gt; w dowolnym punkcie &lt;math&gt;x_0\in\mathbb{R}\, &lt;/math&gt;,...&quot;</title>
		<link rel="alternate" type="text/html" href="http://brain.fuw.edu.pl/edu/index.php?title=Matematyka_1NI/Ci%C4%85g%C5%82o%C5%9B%C4%87_zwyk%C5%82a&amp;diff=1205&amp;oldid=prev"/>
		<updated>2015-05-22T12:30:17Z</updated>

		<summary type="html">&lt;p&gt;Utworzono nową stronę &amp;quot;==Ciągłość zwykła==  &amp;lt;big&amp;gt;&amp;#039;&amp;#039;&amp;#039;&amp;#039;&amp;#039;Zadanie 1&amp;#039;&amp;#039;&amp;#039;&amp;#039;&amp;#039;&amp;lt;/big&amp;gt;  Wykazać ciągłość funkcji &amp;lt;math&amp;gt;f(x)=\cos x\, &amp;lt;/math&amp;gt; w dowolnym punkcie &amp;lt;math&amp;gt;x_0\in\mathbb{R}\, &amp;lt;/math&amp;gt;,...&amp;quot;&lt;/p&gt;
&lt;a href=&quot;http://brain.fuw.edu.pl/edu/index.php?title=Matematyka_1NI/Ci%C4%85g%C5%82o%C5%9B%C4%87_zwyk%C5%82a&amp;amp;diff=1205&quot;&gt;Podgląd zmian&lt;/a&gt;</summary>
		<author><name>Anula</name></author>
		
	</entry>
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