Step-by-Step Calculus Demo: Interactive Paging for Tangents, Limits & Inequaliti
2020-07-19 02:46
This GeoGebra example demonstrates how to use paging and step-by-step display features to progressively present calculus concepts. It covers tangent line construction for function f, visualization of limit processes, and geometric illustration of inequality relationships. Buttons (button1–button6) control step progression, while points A, B, C and transformed point C' are dynamically generated to
In collections
Minority Pi GeoGebra Collection
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.591.0" app="classic" platform="w" id="256def57-f35d-4835-89eb-b5f1f320270f" xsi:noNamespaceSchemaLocation="https://ggb123.cn/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1334" height="497" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.1956521739130435" orientation="1" />
</panes>
<views>
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="true" location="3,1,1" size="372" window="100,100,600,400" />
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 51 | 551 550 11 , 20 22 21 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 , 538 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502" visible="false" inframe="false" stylebar="false" location="1,1,1" size="500" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="16" visible="false" inframe="false" stylebar="true" location="3,1" size="544" window="50,50,500,500" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1" size="1065" window="100,100,600,400" />
<view id="2" visible="true" inframe="false" stylebar="true" location="3" size="261" window="100,100,600,400" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="128" visible="false" inframe="false" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="4097" visible="false" inframe="false" stylebar="true" location="1" size="197" window="100,100,700,550" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
</views>
<toolbar show="false" items="0 39 73 62 | 1 501 67 , 5 19 , 72 75 76 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 14 68 | 30 29 54 32 31 33 | 25 17 26 60 52 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="false" cmd="true" top="true" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="18"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1065" height="497"/>
<coordSystem xZero="168.59997165514443" yZero="383.44544101035314" scale="27.582248854900495" yscale="27.58224885490047"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3"/>
<bgColor r="0" g="51" b="0"/>
<axesColor r="255" g="255" b="255"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<algebraView>
<mode val="1"/>
</algebraView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="numeric" label="n">
<value val="3"/>
<show object="false" label="true"/>
<objColor r="255" g="255" b="255" alpha="0.10000000149011612"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="3" absoluteScreenLocation="true" width="120" x="537" y="37" fixed="false" horizontal="true" showAlgebra="true"/>
<pointSize val="3"/>
<lineStyle thickness="6" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<expression label="text2" exp=""【例题】点A,B,C在同一条直线上,AB=8,BC=2。""/>
<element type="text" label="text2">
<show object="true" label="false" ev="40"/>
<objColor r="255" g="255" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint x="-3.8285482888166538" y="12.342918186305429" z="1"/>
</element>
<expression label="text3" exp=""(1)则AC=_______.""/>
<element type="text" label="text3">
<show object="true" label="false" ev="40"/>
<condition showObject="n ≥ 1"/>
<objColor r="255" g="255" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint x="-1.2544289567236326" y="11.21900692863101" z="1"/>
</element>
<expression label="text5" exp=""(2)若M为AC中点,求MB的长。""/>
<element type="text" label="text5">
<show object="true" label="false" ev="40"/>
<condition showObject="n ≥ 2"/>
<objColor r="255" g="255" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint x="-1.254428956723633" y="9.73254365235194" z="1"/>
</element>
<expression label="text8" exp=""(3)若M、N分别为AC、BC的中点,求MN的长。""/>
<element type="text" label="text8">
<show object="true" label="false" ev="40"/>
<condition showObject="n ≥ 3"/>
<objColor r="255" g="255" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint x="-1.2181737548631677" y="8.354845981654263" z="1"/>
</element>
<element type="point" label="A">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="255" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-0.09426249718874846" y="6.143278668165891" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="B">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="255" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="6.90299146188102" y="6.179533870026356" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Line">
<input a0="A" a1="B"/>
<output a0="f"/>
</command>
<element type="line" label="f">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.036255201860464936" y="6.997253959069768" z="-42.989498488356084"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<expression label="text1" exp=""(1)当C点在点B左边时""/>
<element type="text" label="text1">
<show object="true" label="false" ev="40"/>
<condition showObject="i ≥ 1"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint x="-1.218173754863166" y="3.24286251932868" z="1"/>
</element>
<expression label="text4" exp=""∵AB=8,BC=2""/>
<element type="text" label="text4">
<show object="true" label="true" ev="40"/>
<condition showObject="i ≥ 2"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint x="-0.27553850649107314" y="1.9376752523519347" z="1"/>
</element>
<expression label="text6" exp=""∴AC=AB-BC=6""/>
<element type="text" label="text6">
<show object="true" label="true" ev="40"/>
<condition showObject="i ≥ 3"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint x="-0.3117937083515392" y="0.8137639946775154" z="1"/>
</element>
<command name="Point">
<input a0="f"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="true" label="true" ev="4"/>
<condition showObject="i ≥ 1"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="4.579507779604543" y="6.167495094470519" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="button" label="button1">
<show object="true" label="true"/>
<objColor r="96" g="96" b="96" alpha="1"/>
<layer val="0"/>
<labelOffset x="575" y="97"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue(n,n-1)"/>
<font serif="false" sizeM="1.4" size="8" style="0"/>
<caption val="上一题"/>
</element>
<element type="button" label="button2">
<show object="true" label="true"/>
<objColor r="96" g="96" b="96" alpha="1"/>
<layer val="0"/>
<labelOffset x="576" y="149"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue(n,n+1)"/>
<font serif="false" sizeM="1.4" size="8" style="0"/>
<caption val="下一题"/>
</element>
<element type="numeric" label="i">
<value val="3"/>
<show object="false" label="true"/>
<objColor r="255" g="255" b="255" alpha="0.10000000149011612"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="3" absoluteScreenLocation="true" width="120" x="5" y="409" fixed="false" horizontal="true" showAlgebra="true"/>
<pointSize val="3"/>
<lineStyle thickness="6" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="button" label="button3">
<show object="true" label="true"/>
<objColor r="96" g="96" b="96" alpha="1"/>
<layer val="0"/>
<labelOffset x="32" y="276"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetValue(i,i-1)"/>
<font serif="false" sizeM="1.4" size="8" style="0"/>
<caption val="上一步"/>
</element>
<element type="button" label="button4">
<show object="true" label="true"/>
<objColor r="96" g="96" b="96" alpha="1"/>
<layer val="0"/>
<labelOffset x="33" y="320"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetValue(i,i+1)"/>
<font serif="false" sizeM="1.4" size="8" style="0"/>
<caption val="下一步"/>
</element>
<expression label="text7" exp=""(2)当C点在点B右边时""/>
<element type="text" label="text7">
<show object="true" label="false" ev="40"/>
<condition showObject="e ≥ 1"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint x="6.866736260020554" y="3.0253313081658884" z="1"/>
</element>
<expression label="text9" exp=""∵AB=8,BC'=2""/>
<element type="text" label="text9">
<show object="true" label="false" ev="40"/>
<condition showObject="e ≥ 2"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint x="7.809371508392648" y="1.9739304542124" z="1"/>
</element>
<expression label="text10" exp=""∴AC'=AB+BC'=10""/>
<element type="text" label="text10">
<show object="true" label="false" ev="40"/>
<condition showObject="e ≥ 3"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint x="7.809371508392644" y="0.8862743983984456" z="1"/>
</element>
<element type="numeric" label="e">
<value val="3"/>
<show object="false" label="true"/>
<objColor r="255" g="255" b="255" alpha="0.10000000149011612"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="3" absoluteScreenLocation="true" width="120" x="597" y="267" fixed="false" horizontal="true" showAlgebra="true"/>
<pointSize val="3"/>
<lineStyle thickness="6" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="button" label="button5">
<show object="true" label="true"/>
<objColor r="96" g="96" b="96" alpha="1"/>
<layer val="0"/>
<labelOffset x="578" y="277"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetValue(e,e-1)"/>
<font serif="false" sizeM="1.4" size="8" style="0"/>
<caption val="上一步"/>
</element>
<element type="button" label="button6">
<show object="true" label="true"/>
<objColor r="96" g="96" b="96" alpha="1"/>
<layer val="0"/>
<labelOffset x="579" y="323"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetValue(e,e+1)"/>
<font serif="false" sizeM="1.4" size="8" style="0"/>
<caption val="下一步"/>
</element>
<command name="Point">
<input a0="f"/>
<output a0="C'"/>
</command>
<element type="point" label="C'">
<show object="true" label="true" ev="4"/>
<condition showObject="e ≥ 1"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="9.151317170232858" y="6.191183226028179" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
</construction>
</geogebra>