Interactive Double Integral Visualization
2018-04-07 14:06
This GeoGebra applet provides an interactive tool for calculating and visualizing double integrals. Users can customize the integrand and boundary conditions via input fields. Utilizing commands like Surface and CurveCartesian, it renders 3D surfaces and boundary curves. Powered by Simplify and LaTeX, the system automatically computes the exact value of the double integral and dynamically displays
In collections
Interactive 3D Surfaces in GeoGebra
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.451.0" app="classic" platform="w" id="c9aa6f4e-5781-4202-879d-ec35c7b1f5d1" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1017" height="628" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.30186823992133727" orientation="1" />
</panes>
<views>
<view id="1" visible="false" inframe="true" stylebar="true" location="3,3,2" size="296" window="678,299,600,400" />
<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="1,1" size="300" 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="true" stylebar="true" location="1,3" size="300" window="446,261,600,400" />
<view id="2" visible="false" inframe="false" stylebar="true" location="3" size="263" window="446,266,250,400" />
<view id="16" visible="true" inframe="false" stylebar="true" location="3" size="307" window="50,50,500,500" />
<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="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="128" visible="false" inframe="true" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="4097" visible="false" inframe="true" stylebar="true" location="1" size="490" window="848,220,934,647" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="43" visible="false" inframe="false" stylebar="false" location="1" size="450" window="50,50,500,500" />
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 | 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 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502" visible="true" inframe="false" stylebar="false" location="1" size="700" window="100,100,600,400" />
</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 || 100001 100002 100003 100004 100005 100006 100007 100008 100009 100010 100011 100012 100013 100014 100015 100016 100017 100018 100019 100020 100021 100022 100023 100024 100025 100026 100027 100028 100029 100030 100031 100032 100033 100034 100035 100036 100037 100038 100039 100040 100041 100042 100043 100044 100045 100046 100047 100048 100049 100050 100051 100052 100053 100054 100055 100056 100057 100058 100059 100060 100061 100062 100063 100064 100065 100066 100067 100068 100069" position="1" help="false" />
<input show="false" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="16"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="580" height="469"/>
<coordSystem xZero="79.0000000000001" yZero="164.00000000000003" scale="50.00000000000002" yscale="50.00000000000002"/>
<evSettings axes="true" grid="true" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="0"/>
<axis id="0" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<euclidianView>
<viewNumber viewNo="2"/>
<size width="307" height="626"/>
<coordSystem xZero="127.27445709181352" yZero="300.433125" scale="55.093731594325654" yscale="55.09375"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="1" rightAngleStyle="1" checkboxSize="26" gridType="3"/>
<bgColor r="192" g="192" b="192"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="64" g="64" b="64"/>
<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"/>
<grid distX="1" distY="1" distTheta="0.5235987755982988"/>
</euclidianView>
<kernel>
<uses3D val="true"/>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<euclidianView3D>
<coordSystem xZero="0" yZero="0" zZero="-4.017912215014411" scale="46.557086434392346" xAngle="24" zAngle="420.1584303451275"/>
<evSettings axes="true" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" gridType="3"/>
<axis id="0" show="true" label="" unitLabel="" tickStyle="2" showNumbers="false" positiveAxis="true" selectionAllowed="false"/>
<axis id="1" show="true" label="" unitLabel="" tickStyle="2" showNumbers="false" positiveAxis="true" selectionAllowed="false"/>
<axis id="2" show="false" label="" unitLabel="" tickStyle="2" showNumbers="false" positiveAxis="true" selectionAllowed="false"/>
<plate show="false"/>
<bgColor r="255" g="255" b="255"/>
<clipping use="false" show="false" size="1"/>
<projection type="1"/>
</euclidianView3D>
<construction title="" author="" date="">
<expression label ="f" exp="f(x, y) = x^(2) + y^(2) - (sqrt(2) * y) + 1 / 2"/>
<element type="functionNVar" label="f">
<show object="false" label="false" ev="4"/>
<objColor r="204" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
</element>
<expression label ="g" exp="g(x, y) = 4 - (sqrt(2) * y)"/>
<element type="functionNVar" label="g">
<show object="false" label="false" ev="4"/>
<objColor r="153" g="51" b="255" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
</element>
<command name="Solve">
<input a0="f(x, y) = g(x, y)"/>
<output a0="xs"/>
</command>
<element type="list" label="xs">
<objColor r="0" g="100" b="0" alpha="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Zip">
<input a0="RightSide[eq]" a1="eq" a2="xs"/>
<output a0="equs"/>
</command>
<element type="list" label="equs">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Element" type="functionnvar">
<input a0="equs" a1="1"/>
<output a0="func1"/>
</command>
<element type="functionNVar" label="func1">
<show object="false" label="true" ev="4"/>
<objColor r="204" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
</element>
<expression label="fx1" exp="fx1(x) = func1(0, x)" />
<element type="function" label="fx1">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
</element>
<command name="Element" type="functionnvar">
<input a0="equs" a1="2"/>
<output a0="func2"/>
</command>
<element type="functionNVar" label="func2">
<show object="false" label="true" ev="4"/>
<objColor r="204" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
</element>
<expression label="fx2" exp="fx2(x) = func2(0, x)" />
<element type="function" label="fx2">
<show object="false" label="true" ev="4"/>
<objColor r="204" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
</element>
<expression label ="ts" exp="0.4"/>
<element type="numeric" label="ts">
<value val="0.4"/>
<symbolic val="true" />
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<expression label ="th" exp="1"/>
<element type="numeric" label="th">
<value val="1"/>
<symbolic val="true" />
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<expression label ="tw" exp="0.3"/>
<element type="numeric" label="tw">
<value val="0.3"/>
<symbolic val="true" />
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<expression label ="tp" exp="0.1"/>
<element type="numeric" label="tp">
<value val="0.1"/>
<symbolic val="true" />
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<expression label ="i" exp="(1, 0, 0)" type="vector"/>
<element type="vector3d" label="i">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="1" y="0" z="0" w="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
</element>
<expression label="Δ" exp="Δ(x, y) = g(x, y) - f(x, y)" />
<element type="functionNVar" label="Δ">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
</element>
<command name="Simplify">
<input a0="Δ"/>
<output a0="simpΔ"/>
</command>
<element type="functionNVar" label="simpΔ">
<show object="false" label="false" ev="11"/>
<objColor r="204" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
</element>
<command name="LaTeX">
<input a0="simpΔ" a1="true" a2="false"/>
<output a0="latexDZ2"/>
</command>
<element type="text" label="latexDZ2">
<symbolic val="true" />
<show object="false" label="true" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="0" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<startPoint x="0" y="0" z="1"/>
</element>
<expression label="txtwDZ" exp="x(Corner[latexDZ2, 2] - Corner[latexDZ2, 1])" />
<element type="numeric" label="txtwDZ">
<value val="2.4999999999999987"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label ="O" exp="(0, 0, 0)" type="point"/>
<element type="point3d" label="O">
<show object="false" label="false" ev="5"/>
<objColor r="0" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<coords x="0" y="0" z="0" w="1"/>
<pointSize val="5"/>
</element>
<expression label="txtY" exp=""y""/>
<element type="text" label="txtY">
<show object="true" label="false" ev="21"/>
<condition showObject="showLabels"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<startPoint exp="Y"/>
<labelOffset x="-31" y="-6"/>
</element>
<expression label ="markH" exp="1"/>
<element type="numeric" label="markH">
<value val="1"/>
<symbolic val="true" />
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<expression label ="j" exp="(0, 1, 0)" type="vector"/>
<element type="vector3d" label="j">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0" y="1" z="0" w="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
</element>
<expression label ="k" exp="(0, 0, 1)" type="vector"/>
<element type="vector3d" label="k">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0" y="0" z="1" w="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
</element>
<element type="boolean" label="showG">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="67" y="240"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="show g(x, y)"/>
</element>
<expression label ="pointing" exp="(1.5 * (-1, 1, 2))" type="vector"/>
<element type="vector3d" label="pointing">
<show object="false" label="false" ev="5"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<selectionAllowed val="false"/>
<coords x="-1.5" y="1.5" z="3" w="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
</element>
<command name="Textfield">
<input a0="f"/>
<output a0="inputF"/>
</command>
<element type="textfield" label="inputF">
<show object="true" label="true" ev="3"/>
<objColor r="255" g="0" b="0" alpha="1"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelOffset x="17" y="25"/>
<labelMode val="3"/>
<auxiliary val="true"/>
<linkedGeo exp="f"/>
<length val="15"/>
<caption val="f(x, y) ="/>
</element>
<command name="Textfield">
<input a0="g"/>
<output a0="inputG"/>
</command>
<element type="textfield" label="inputG">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="255" alpha="1"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelOffset x="12" y="69"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<linkedGeo exp="g"/>
<length val="15"/>
<caption val="g(x, y) ="/>
</element>
<command name="LaTeX">
<input a0="f" a1="true" a2="false"/>
<output a0="latexF"/>
</command>
<element type="text" label="latexF">
<show object="false" label="true" ev="11"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1" size="0" style="0"/>
<startPoint x="0.7188357088090399" y="-0.5706682446562423" z="1"/>
</element>
<expression label="text5" exp=""" + (LaTeX[latexF]) + """ />
<element type="text" label="text5">
<show object="true" label="false" ev="5"/>
<condition showObject="showLabels ∧ showSection"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="0" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<startPoint exp="PinZ1"/>
<labelOffset x="10" y="-38"/>
</element>
<command name="LaTeX">
<input a0="g" a1="true" a2="false"/>
<output a0="latexG"/>
</command>
<element type="text" label="latexG">
<show object="false" label="true" ev="11"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1" size="0" style="0"/>
<startPoint x="1.4571886699364247" y="-1.185962378929063" z="1"/>
</element>
<expression label="text4" exp=""" + (LaTeX[latexG]) + """ />
<element type="text" label="text4">
<show object="true" label="false" ev="5"/>
<condition showObject="showLabels ∧ showSection"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="0" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<startPoint exp="PinZ2"/>
<labelOffset x="8" y="-32"/>
</element>
<command name="LaTeX">
<input a0="simpΔ" a1="true" a2="false"/>
<output a0="latexDZ"/>
</command>
<element type="text" label="latexDZ">
<show object="false" label="true" ev="9"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1" size="0" style="0"/>
<startPoint x="1.4161690609849034" y="-0.4681192222774389" z="1"/>
</element>
<expression label="text6" exp=""" + (LaTeX[latexDZ]) + """ />
<element type="text" label="text6">
<show object="true" label="false" ev="5"/>
<condition showObject="showLabels ∧ showSection"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="0" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<startPoint exp="PinDZM2"/>
<labelOffset x="-26" y="14"/>
</element>
<expression label="txtX" exp=""x""/>
<element type="text" label="txtX">
<show object="true" label="false" ev="21"/>
<condition showObject="showLabels"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<startPoint exp="X"/>
<labelOffset x="15" y="-4"/>
</element>
<expression label="equFG" exp="equFG: f(x, y) - g(x, y) = 0" type="conic" />
<element type="conic" label="equFG">
<show object="true" label="false" ev="5"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="3" type="0" typeHidden="2"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-3.5" A3="0" A4="0" A5="0"/>
<eqnStyle style="implicit"/>
</element>
<command name="Sequence">
<input a0="Point[equFG, t]" a1="t" a2="0" a3="1" a4="0.02"/>
<output a0="pts"/>
</command>
<element type="list" label="pts">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Min">
<input a0="y(pts)"/>
<output a0="ymin"/>
</command>
<element type="numeric" label="ymin">
<value val="-1.8671370403107364"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="Max">
<input a0="x(pts)"/>
<output a0="xmax"/>
</command>
<element type="numeric" label="xmax">
<value val="1.8708286933869707"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="C2" exp="(xmax, ymin)" type="point" />
<element type="point" label="C2">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.8708286933869707" y="-1.8671370403107364" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Max">
<input a0="y(pts)"/>
<output a0="ymax"/>
</command>
<element type="numeric" label="ymax">
<value val="1.8671370403107366"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="C3" exp="(xmax, ymax)" type="point" />
<element type="point" label="C3">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.8708286933869707" y="1.8671370403107366" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="C2" a1="C3"/>
<output a0="segY"/>
</command>
<element type="segment" label="segY">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-3.734274080621473" y="0" z="6.986187098997901"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="segY"/>
<output a0="Y"/>
</command>
<element type="point" label="Y">
<show object="true" label="false" ev="4"/>
<objColor r="102" g="204" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="1.8708286933869707" y="-0.8715036997563383" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="b" exp="y(Y)" />
<element type="numeric" label="b">
<value val="-0.8715036997563383"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="a2" exp="fx2(b)" />
<element type="numeric" label="a2">
<value val="1.6554399117186387"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="X2" exp="(a2, ymax)" type="point" />
<element type="point" label="X2">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.6554399117186387" y="1.8671370403107366" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="a1" exp="fx1(b)" />
<element type="numeric" label="a1">
<value val="-1.6554399117186387"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="X1" exp="(a1, ymax)" type="point" />
<element type="point" label="X1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.6554399117186387" y="1.8671370403107366" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="equFG"/>
<output a0="P0"/>
</command>
<element type="point" label="P0">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-1.3392826487717497" y="1.3062626025033885" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="Pf" exp="P0 + (f(x(P0), y(P0)) * k)" type="point" />
<element type="point3d" label="Pf">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.3392826487717497" y="1.3062626025033885" z="2.152665711518932" w="1"/>
<pointSize val="3"/>
</element>
<command name="Locus">
<input a0="Pf" a1="P0"/>
<output a0="boundary"/>
</command>
<element type="locus" label="boundary">
<show object="true" label="false" ev="5"/>
<condition showObject="showF"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<lineStyle thickness="3" type="0" typeHidden="2"/>
</element>
<command name="Zip">
<input a0="LaTeX[RightSide[ans]]" a1="ans" a2="xs"/>
<output a0="latexAns"/>
</command>
<element type="list" label="latexAns">
<show object="false" label="true" ev="9"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
<symbolic val="true" />
</element>
<expression label="text2" exp=""" + (LaTeX[latexAns(1)]) + """ />
<element type="text" label="text2">
<show object="true" label="false" ev="5"/>
<condition showObject="showLabels"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="0" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="0.7" size="-5" style="1"/>
<startPoint exp="PinX1"/>
<labelOffset x="8" y="12"/>
</element>
<expression label="text3" exp=""" + (LaTeX[latexAns(2)]) + """ />
<element type="text" label="text3">
<show object="true" label="true" ev="5"/>
<condition showObject="showLabels"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="0" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="0.7" size="-5" style="1"/>
<startPoint exp="PinX2"/>
<labelOffset x="5" y="13"/>
</element>
<element type="boolean" label="reversed">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="67" y="130"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="f2" exp="f2(x, y) = f(x, y) / If[reversed, g(x, y) < f(x, y), f(x, y) ≤ g(x, y)]" />
<element type="functionNVar" label="f2">
<show object="false" label="false" ev="4"/>
<condition showObject="showF"/>
<objColor r="255" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="1" type="20" typeHidden="2"/>
</element>
<expression label="g2" exp="g2(x, y) = g(x, y) / If[reversed, g(x, y) < f(x, y), f(x, y) ≤ g(x, y)]" />
<element type="functionNVar" label="g2">
<show object="true" label="false" ev="4"/>
<condition showObject="showG"/>
<objColor r="102" g="153" b="255" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="1" type="20" typeHidden="2"/>
</element>
<expression label="Δ2" exp="Δ2(x, y) = Δ(x, y) / If[reversed, g(x, y) < f(x, y), f(x, y) ≤ g(x, y)]" />
<element type="functionNVar" label="Δ2">
<show object="true" label="false" ev="5"/>
<condition showObject="showDZ"/>
<objColor r="102" g="204" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="1" type="20" typeHidden="2"/>
</element>
<element type="boolean" label="showDZ">
<value val="true"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="67" y="295"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="show (g - f)"/>
</element>
<element type="boolean" label="showLabels">
<value val="true"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="67" y="406"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="show labels"/>
</element>
<command name="Min">
<input a0="x(pts)"/>
<output a0="xmin"/>
</command>
<element type="numeric" label="xmin">
<value val="-1.8708286933869707"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="C1" exp="(xmin, ymin)" type="point" />
<element type="point" label="C1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.8708286933869707" y="-1.8671370403107364" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="C4" exp="(xmin, ymax)" type="point" />
<element type="point" label="C4">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.8708286933869707" y="1.8671370403107366" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="{C1, C2, C3, C4}"/>
<output a0="box"/>
</command>
<element type="polygon" label="box">
<lineStyle thickness="2" type="20" typeHidden="2"/>
<show object="true" label="false" ev="5"/>
<objColor r="64" g="64" b="64" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<command name="Segment">
<input a0="X1" a1="X2"/>
<output a0="segX"/>
</command>
<element type="segment" label="segX">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="3.3108798234372774" z="-6.181866354357212"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="segX"/>
<output a0="X"/>
</command>
<element type="point" label="X">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-0.7387798270891882" y="1.8671370403107366" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="a" exp="x(X)" />
<element type="numeric" label="a">
<value val="-0.7387798270891882"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<cascell>
<cellPair>
<inputCell>
<expression value="newa1=Substitute(RightSide(xs(1)), y, newb )" eval="Evaluate(newa1 = Substitute(RightSide(xs(1)),y,b))" evalCmd=""/>
</inputCell>
<outputCell>
<expression value="fx1(((-783345)) / 898843) = (((-1)) / 1797686 * sqrt(8856344784986))" native="true"/>
</outputCell>
</cellPair>
</cascell>
<cascell>
<cellPair>
<inputCell>
<expression value="newa2=Substitute(RightSide(xs(2)), y, newb )" eval="Evaluate(newa2 = Substitute(RightSide(xs(2)),y,b))" evalCmd=""/>
</inputCell>
<outputCell>
<expression value="fx2(((-783345)) / 898843) = (1 / 1797686 * sqrt(8856344784986))" native="true"/>
</outputCell>
</cellPair>
</cascell>
<command name="CurveCartesian">
<input a0="(t, b, f(t, b))" a1="t" a2="a1" a3="a2"/>
<output a0="fxb"/>
</command>
<element type="curvecartesian3d" label="fxb">
<show object="true" label="false" ev="4"/>
<condition showObject="showSection"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
</element>
<command name="CurveCartesian">
<input a0="(t, b, g(t, b))" a1="t" a2="a1" a3="a2"/>
<output a0="gxb"/>
</command>
<element type="curvecartesian3d" label="gxb">
<show object="true" label="false" ev="5"/>
<condition showObject="showSection"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="3" type="0" typeHidden="2"/>
</element>
<expression label="XY" exp="(a, b)" type="point" />
<element type="point" label="XY">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.7387798270891882" y="-0.8715036997563383" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="z1" exp="f(a, b)" />
<element type="numeric" label="z1">
<value val="3.0378066834566604"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="z2" exp="g(a, b)" />
<element type="numeric" label="z2">
<value val="5.232492351853743"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="Z1" exp="(a, b, z1)" type="point" />
<element type="point3d" label="Z1">
<show object="true" label="false" ev="5"/>
<condition showObject="showSection"/>
<objColor r="102" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="-0.7387798270891882" y="-0.8715036997563383" z="3.0378066834566604" w="1"/>
<pointSize val="4"/>
</element>
<expression label="Z2" exp="(a, b, z2)" type="point" />
<element type="point3d" label="Z2">
<show object="true" label="false" ev="5"/>
<condition showObject="showSection"/>
<objColor r="102" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="-0.7387798270891882" y="-0.8715036997563383" z="5.232492351853743" w="1"/>
<pointSize val="4"/>
</element>
<command name="Segment">
<input a0="Z1" a1="Z2"/>
<output a0="segZ"/>
</command>
<element type="segment3d" label="segZ">
<show object="true" label="false" ev="5"/>
<condition showObject="showSection"/>
<objColor r="102" g="204" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="4" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="X" a1="XY"/>
<output a0="segXY"/>
</command>
<element type="segment" label="segXY">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.738640740067075" y="0" z="2.02325253240616"/>
<lineStyle thickness="1" type="20" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="XY" a1="Z1"/>
<output a0="segZ1"/>
</command>
<element type="segment3d" label="segZ1">
<show object="true" label="false" ev="4"/>
<condition showObject="showSection"/>
<objColor r="0" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="1" type="20" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="Z3" exp="(a1, b, f(a1, b))" type="point" />
<element type="point3d" label="Z3">
<show object="true" label="false" ev="5"/>
<condition showObject="showSection"/>
<objColor r="102" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="-1.6554399117186387" y="-0.8715036997563383" z="5.232492351853743" w="1"/>
<pointSize val="4"/>
</element>
<expression label="Z4" exp="(a2, b, f(a2, b))" type="point" />
<element type="point3d" label="Z4">
<show object="true" label="false" ev="5"/>
<condition showObject="showSection"/>
<objColor r="102" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="1.6554399117186387" y="-0.8715036997563383" z="5.232492351853743" w="1"/>
<pointSize val="4"/>
</element>
<command name="Segment">
<input a0="Z1" a1="Z1 + pointing"/>
<output a0="ptrZ1"/>
</command>
<element type="segment3d" label="ptrZ1">
<show object="true" label="false" ev="4"/>
<condition showObject="showLabels ∧ showSection"/>
<objColor r="102" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="20" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="PinZ1" exp="Z1 + pointing" type="point" />
<element type="point3d" label="PinZ1">
<show object="true" label="false" ev="5"/>
<condition showObject="showLabels ∧ showSection"/>
<objColor r="102" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="-2.2387798270891883" y="0.6284963002436617" z="6.03780668345666" w="1"/>
<pointSize val="3"/>
</element>
<expression label="PinZ2" exp="Z2 + pointing" type="point" />
<element type="point3d" label="PinZ2">
<show object="false" label="false" ev="5"/>
<condition showObject="showLabels ∧ showSection"/>
<objColor r="102" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="-2.2387798270891883" y="0.6284963002436617" z="8.232492351853743" w="1"/>
<pointSize val="3"/>
</element>
<command name="Segment">
<input a0="Z2" a1="PinZ2"/>
<output a0="ptrZ2"/>
</command>
<element type="segment3d" label="ptrZ2">
<show object="false" label="false" ev="4"/>
<condition showObject="showLabels ∧ showSection"/>
<objColor r="102" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="20" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="markX" exp="xmax + 0.5" />
<element type="numeric" label="markX">
<value val="2.3708286933869704"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="PinZ22" exp="(markX, b, z2)" type="point" />
<element type="point3d" label="PinZ22">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.3708286933869704" y="-0.8715036997563383" z="5.232492351853743" w="1"/>
<pointSize val="3"/>
</element>
<command name="Segment">
<input a0="Z2" a1="PinZ22"/>
<output a0="ptrZ22"/>
</command>
<element type="segment3d" label="ptrZ22">
<show object="true" label="false" ev="4"/>
<condition showObject="showSection ∧ showLabels"/>
<objColor r="0" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="20" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="PinZ12" exp="(markX, b, z1)" type="point" />
<element type="point3d" label="PinZ12">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.3708286933869704" y="-0.8715036997563383" z="3.0378066834566604" w="1"/>
<pointSize val="3"/>
</element>
<command name="Segment">
<input a0="Z1" a1="PinZ12"/>
<output a0="ptrZ12"/>
</command>
<element type="segment3d" label="ptrZ12">
<show object="true" label="false" ev="4"/>
<condition showObject="showSection ∧ showLabels"/>
<objColor r="0" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="20" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="DimensionArrows">
<input a0="PinZ22" a1="PinZ12" a2="i" a3="tp" a4="tw" a5="th" a6="ts"/>
<output a0="ddz_1" a1="ddz_2" a2="PinDZM"/>
</command>
<element type="polygon3d" label="ddz_1">
<lineStyle thickness="1" type="0" typeHidden="2" opacity="178"/>
<show object="true" label="false" ev="5"/>
<condition showObject="showSection ∧ showLabels"/>
<objColor r="102" g="0" b="153" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<element type="polygon3d" label="ddz_2">
<lineStyle thickness="1" type="0" typeHidden="2" opacity="178"/>
<show object="true" label="false" ev="5"/>
<condition showObject="showSection ∧ showLabels"/>
<objColor r="102" g="0" b="153" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<element type="point3d" label="PinDZM">
<show object="true" label="false" ev="4"/>
<condition showObject="showSection ∧ showLabels"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.6208286933869704" y="-0.8715036997563383" z="4.135149517655202" w="1"/>
<pointSize val="2"/>
<caption val="arrow center"/>
</element>
<expression label="PinDZM2" exp="PinDZM + (txtwDZ * i)" type="point" />
<element type="point3d" label="PinDZM2">
<show object="true" label="false" ev="5"/>
<condition showObject="showLabels ∧ showSection"/>
<objColor r="102" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="5.120828693386969" y="-0.8715036997563383" z="4.135149517655202" w="1"/>
<pointSize val="3"/>
</element>
<command name="Segment">
<input a0="PinDZM" a1="PinDZM2"/>
<output a0="ptrDz"/>
</command>
<element type="segment3d" label="ptrDz">
<show object="true" label="false" ev="5"/>
<condition showObject="showLabels ∧ showSection"/>
<objColor r="102" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="2" type="20" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="secH" exp="z(CornerThreeD[-1, 5] - CornerThreeD[-1, 1])" />
<element type="numeric" label="secH">
<value val="9.507657779370575"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="S1" exp="(xmin, b, 0)" type="point" />
<element type="point3d" label="S1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.8708286933869707" y="-0.8715036997563383" z="0" w="1"/>
<pointSize val="3"/>
</element>
<expression label="S2" exp="(xmax, b, 0)" type="point" />
<element type="point3d" label="S2">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.8708286933869707" y="-0.8715036997563383" z="0" w="1"/>
<pointSize val="3"/>
</element>
<expression label="S3" exp="(xmax, b, secH)" type="point" />
<element type="point3d" label="S3">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.8708286933869707" y="-0.8715036997563383" z="9.507657779370575" w="1"/>
<pointSize val="3"/>
</element>
<expression label="S4" exp="(xmin, b, secH)" type="point" />
<element type="point3d" label="S4">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.8708286933869707" y="-0.8715036997563383" z="9.507657779370575" w="1"/>
<pointSize val="3"/>
</element>
<command name="Polygon">
<input a0="{S1, S2, S3, S4}"/>
<output a0="secY"/>
</command>
<element type="polygon3d" label="secY">
<lineStyle thickness="1" type="0" typeHidden="2"/>
<show object="true" label="false" ev="5"/>
<condition showObject="showSectionPlane"/>
<objColor r="0" g="0" b="0" alpha="0.05000000074505806"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<expression label="X1b" exp="(a1, b)" type="point" />
<element type="point" label="X1b">
<show object="true" label="false" ev="5"/>
<objColor r="102" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="-1.6554399117186387" y="-0.8715036997563383" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="X2b" exp="(a2, b)" type="point" />
<element type="point" label="X2b">
<show object="true" label="false" ev="5"/>
<objColor r="102" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="1.6554399117186387" y="-0.8715036997563383" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="X1b" a1="Z3"/>
<output a0="segA1"/>
</command>
<element type="segment3d" label="segA1">
<show object="true" label="false" ev="5"/>
<condition showObject="showSection"/>
<objColor r="102" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="2" type="20" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="X2b" a1="Z4"/>
<output a0="segA2"/>
</command>
<element type="segment3d" label="segA2">
<show object="true" label="false" ev="5"/>
<condition showObject="showSection"/>
<objColor r="102" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="2" type="20" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="markY" exp="ymax + 1" />
<element type="numeric" label="markY">
<value val="2.8671370403107366"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="PinX1" exp="(a1, markY)" type="point" />
<element type="point" label="PinX1">
<show object="true" label="false" ev="5"/>
<condition showObject="showLabels"/>
<objColor r="102" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="-1.6554399117186387" y="2.8671370403107366" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="X1b" a1="PinX1"/>
<output a0="ptrX1"/>
</command>
<element type="segment" label="ptrX1">
<show object="true" label="false" ev="4"/>
<condition showObject="showLabels"/>
<objColor r="102" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-3.738640740067075" y="0" z="-6.189095096684344"/>
<lineStyle thickness="2" type="20" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="PinX2" exp="(a2, markY)" type="point" />
<element type="point" label="PinX2">
<show object="true" label="false" ev="5"/>
<condition showObject="showLabels"/>
<objColor r="102" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="1.6554399117186387" y="2.8671370403107366" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="X2b" a1="PinX2"/>
<output a0="ptrX2"/>
</command>
<element type="segment" label="ptrX2">
<show object="true" label="false" ev="4"/>
<condition showObject="showLabels"/>
<objColor r="102" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-3.738640740067075" y="0" z="6.189095096684344"/>
<lineStyle thickness="2" type="20" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Surface">
<input a0="t" a1="b + 0.01" a2="((1 - s) * g(t, b)) + (s * f(t, b))" a3="t" a4="a1" a5="a2" a6="s" a7="0" a8="1"/>
<output a0="surfY"/>
</command>
<element type="surfacecartesian3d" label="surfY">
<show object="true" label="false" ev="4"/>
<condition showObject="showSection"/>
<objColor r="204" g="102" b="255" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="0" type="0" typeHidden="2"/>
</element>
<command name="Segment">
<input a0="X2" a1="X2b"/>
<output a0="segX2"/>
</command>
<element type="segment" label="segX2">
<show object="false" label="false" ev="5"/>
<objColor r="102" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="2.738640740067075" y="0" z="-4.533655184965706"/>
<lineStyle thickness="2" type="20" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="X1" a1="X1b"/>
<output a0="segX1"/>
</command>
<element type="segment" label="segX1">
<show object="false" label="false" ev="5"/>
<objColor r="102" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="2.738640740067075" y="0" z="4.533655184965706"/>
<lineStyle thickness="2" type="20" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="boolean" label="showF">
<value val="true"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="67" y="185"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="show f(x, y)"/>
</element>
<element type="boolean" label="showSectionPlane">
<value val="true"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="67" y="516"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="show section plane"/>
</element>
<element type="boolean" label="showSection">
<value val="true"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="67" y="461"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="show cross section"/>
</element>
<command name="Segment">
<input a0="X1b" a1="X2b"/>
<output a0="segX1X2"/>
</command>
<element type="segment" label="segX1X2">
<show object="true" label="false" ev="5"/>
<condition showObject="¬showSectionPlane"/>
<objColor r="102" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="0" y="3.3108798234372774" z="2.8854440155741994"/>
<lineStyle thickness="2" type="20" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="newa2" exp="fx2(b)" />
<element type="numeric" label="newa2">
<value val="1.6554399117186387"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="newa1" exp="fx1(b)" />
<element type="numeric" label="newa1">
<value val="-1.6554399117186387"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
</construction>
</geogebra>