範例：數值二重積分

運算子 > 微積分運算子 > 範例：數值二重積分

範例：數值二重積分

計算 x-y 平面之區域的實數函數積分，以計算該範圍的質量及質量中心。

1. 定義要計算積分的區域邊界。讓所有 x 成為 a < x < b 且 c(x) < y < d(x)。

按一下以複製此運算式

按一下以複製此運算式

按一下以複製此運算式

按一下以複製此運算式

2. 繪製要計算積分的區域。

按一下以複製此運算式

<region id="ID0EUO4R" top="384" left="19.2" xml:lang="zh_TW" height="25.6" width="118.783333333333" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="118" xml:lang="zh_TW">
    <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">
      <id xml:space="preserve" xml:lang="zh_TW" label="None">x</id>
      <range xml:lang="zh_TW">
        <sequence xml:lang="zh_TW">
          <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">a</id>
          <apply xml:lang="zh_TW">
            <plus xml:lang="zh_TW" />
            <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">a</id>
            <real xml:lang="zh_TW">0.01</real>
          </apply>
        </sequence>
        <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">b</id>
      </range>
    </define>
    <resultFormat xml:lang="zh_TW">
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" />
    </resultFormat>
  </math>
</region>

按一下以複製此運算式

<region id="ID0EGP4R" top="422.4" left="19.2" xml:lang="zh_TW" height="25.6" width="184.573333333333" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="119" xml:lang="zh_TW">
    <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">
      <id xml:space="preserve" xml:lang="zh_TW" label="None">y</id>
      <range xml:lang="zh_TW">
        <sequence xml:lang="zh_TW">
          <apply xml:lang="zh_TW">
            <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">c</id>
            <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">a</id>
          </apply>
          <apply xml:lang="zh_TW">
            <plus xml:lang="zh_TW" />
            <apply xml:lang="zh_TW">
              <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">c</id>
              <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">a</id>
            </apply>
            <real xml:lang="zh_TW">0.01</real>
          </apply>
        </sequence>
        <apply xml:lang="zh_TW">
          <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">d</id>
          <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">a</id>
        </apply>
      </range>
    </define>
    <resultFormat xml:lang="zh_TW">
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" />
    </resultFormat>
  </math>
</region>

按一下以複製此運算式

<region id="ID0EYP4R" top="460.8" left="19.2" xml:lang="zh_TW" height="25.6" width="180.95" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="120" xml:lang="zh_TW">
    <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">
      <id xml:space="preserve" xml:lang="zh_TW" label="None">z</id>
      <range xml:lang="zh_TW">
        <sequence xml:lang="zh_TW">
          <apply xml:lang="zh_TW">
            <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">c</id>
            <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">b</id>
          </apply>
          <apply xml:lang="zh_TW">
            <plus xml:lang="zh_TW" />
            <apply xml:lang="zh_TW">
              <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">c</id>
              <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">b</id>
            </apply>
            <real xml:lang="zh_TW">0.01</real>
          </apply>
        </sequence>
        <apply xml:lang="zh_TW">
          <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">d</id>
          <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">b</id>
        </apply>
      </range>
    </define>
    <resultFormat xml:lang="zh_TW">
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" />
    </resultFormat>
  </math>
</region>

按一下以複製此運算式

<region id="ID0EKQ4R" top="480" left="19.2" xml:lang="zh_TW" height="287.628571428571" width="594.971428571429" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot background-type="white" origin-positioning="false" xml:lang="zh_TW" show-axis-expressions="true">
    <xyPlot xml:lang="zh_TW">
      <title class="- topic/title " xml:lang="zh_TW" toc="yes" wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" />
      <legend xml:lang="zh_TW" />
      <traces xml:lang="zh_TW">
        <trace resultRef="121" xml:lang="zh_TW">
          <traceStyle color="#FF0000FF" symbol="none" line-weight="1" line-style="Solid" xml:lang="zh_TW">線條</traceStyle>
        </trace>
        <trace resultRef="122" xml:lang="zh_TW">
          <traceStyle color="#FF0C0C0C" symbol="none" line-weight="1" line-style="Solid" xml:lang="zh_TW">線條</traceStyle>
        </trace>
        <trace resultRef="123" xml:lang="zh_TW">
          <traceStyle color="#FF800080" symbol="none" line-weight="1" line-style="Solid" xml:lang="zh_TW">線條</traceStyle>
        </trace>
        <trace resultRef="124" xml:lang="zh_TW">
          <traceStyle color="#FF008000" symbol="none" line-weight="1" line-style="Solid" xml:lang="zh_TW">線條</traceStyle>
        </trace>
      </traces>
      <graph-size width="475.771428571429" height="230.028571428571" xml:lang="zh_TW" />
      <axes xml:lang="zh_TW">
        <xAxis rank="1" legend-position="PlotBoundaryBottom" start="-0.1" end="1" xml:lang="zh_TW">
          <axisLine position="origin" positionticmark="3" legendWidth="170.93" xml:lang="zh_TW" />
          <axisGrid xml:lang="zh_TW">
            <gridFrequency xml:lang="zh_TW">12</gridFrequency>
            <gridLabels display="true" xml:lang="zh_TW" />
            <gridLines xml:lang="zh_TW" />
            <tickMarks display="true" xml:lang="zh_TW" />
          </axisGrid>
          <axisLabel xml:lang="zh_TW" />
          <markers xml:lang="zh_TW" />
          <numberFormat xml:lang="zh_TW">
            <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" xml:lang="zh_TW" />
          </numberFormat>
          <plotEquations xml:lang="zh_TW">
            <plotEquation xml:lang="zh_TW">
              <math resultRef="127" xml:lang="zh_TW">
                <id xml:space="preserve" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">a</id>
              </math>
              <math resultRef="128" xml:lang="zh_TW">
                <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
            <plotEquation xml:lang="zh_TW">
              <math resultRef="129" xml:lang="zh_TW">
                <id xml:space="preserve" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">b</id>
              </math>
              <math resultRef="130" xml:lang="zh_TW">
                <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
            <plotEquation xml:lang="zh_TW">
              <math resultRef="131" xml:lang="zh_TW">
                <id xml:space="preserve" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">x</id>
              </math>
              <math resultRef="132" xml:lang="zh_TW">
                <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true" xml:lang="zh_TW">
            <startValue xml:lang="zh_TW" resultRef="126">
              <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">-0.1</real>
            </startValue>
            <endValue xml:lang="zh_TW">
              <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </xAxis>
        <yAxis rank="1" legend-position="PlotBoundaryLeft" start="-0.6" end="1.2" xml:lang="zh_TW">
          <axisLine position="ticknumberlock" positionticmark="0" legendWidth="83.74" xml:lang="zh_TW" />
          <axisGrid xml:lang="zh_TW">
            <gridFrequency xml:lang="zh_TW">10</gridFrequency>
            <gridLabels display="true" xml:lang="zh_TW" />
            <gridLines xml:lang="zh_TW" />
            <tickMarks display="true" xml:lang="zh_TW" />
          </axisGrid>
          <axisLabel xml:lang="zh_TW" />
          <markers xml:lang="zh_TW" />
          <numberFormat xml:lang="zh_TW">
            <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" xml:lang="zh_TW" />
          </numberFormat>
          <plotEquations xml:lang="zh_TW">
            <plotEquation xml:lang="zh_TW">
              <math resultRef="139" xml:lang="zh_TW">
                <id xml:space="preserve" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">y</id>
              </math>
              <math resultRef="140" xml:lang="zh_TW">
                <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
            <plotEquation xml:lang="zh_TW">
              <math resultRef="141" xml:lang="zh_TW">
                <id xml:space="preserve" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">z</id>
              </math>
              <math resultRef="142" xml:lang="zh_TW">
                <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
            <plotEquation xml:lang="zh_TW">
              <math resultRef="143" xml:lang="zh_TW">
                <apply xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">
                  <id xml:space="preserve" xml:lang="zh_TW">c</id>
                  <id xml:space="preserve" xml:lang="zh_TW">x</id>
                </apply>
              </math>
              <math resultRef="144" xml:lang="zh_TW">
                <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
            <plotEquation xml:lang="zh_TW">
              <math resultRef="145" xml:lang="zh_TW">
                <apply xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">
                  <id xml:space="preserve" xml:lang="zh_TW">d</id>
                  <id xml:space="preserve" xml:lang="zh_TW">x</id>
                </apply>
              </math>
              <math resultRef="146" xml:lang="zh_TW">
                <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true" xml:lang="zh_TW">
            <startValue xml:lang="zh_TW" resultRef="134">
              <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">-0.6</real>
            </startValue>
            <secondTickValue resultRef="136" xml:lang="zh_TW">
              <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">-0.4</real>
            </secondTickValue>
            <endValue xml:lang="zh_TW" resultRef="138">
              <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">1</real>
            </endValue>
          </xyDomain>
        </yAxis>
      </axes>
    </xyPlot>
  </plot>
</region>

3. 定義要求解積分的實數函數。

按一下以複製此運算式

<region id="ID0E6R4R" top="844.8" left="19.2" xml:lang="zh_TW" height="33.0289335273266" width="129.882666636904" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="165" xml:lang="zh_TW">
    <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">
      <function xml:lang="zh_TW">
        <id xml:space="preserve" xml:lang="zh_TW" label="None">f</id>
        <boundVars xml:lang="zh_TW">
          <id xml:space="preserve" xml:lang="zh_TW" label="None">x</id>
          <id xml:space="preserve" xml:lang="zh_TW" label="None">y</id>
        </boundVars>
      </function>
      <apply xml:lang="zh_TW">
        <nthRoot xml:lang="zh_TW" />
        <placeholder xml:lang="zh_TW" />
        <apply xml:lang="zh_TW">
          <plus xml:lang="zh_TW" />
          <apply xml:lang="zh_TW">
            <pow xml:lang="zh_TW" />
            <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">x</id>
            <real xml:lang="zh_TW">2</real>
          </apply>
          <apply xml:lang="zh_TW">
            <pow xml:lang="zh_TW" />
            <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">y</id>
            <real xml:lang="zh_TW">2</real>
          </apply>
        </apply>
      </apply>
    </define>
    <resultFormat xml:lang="zh_TW">
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" />
    </resultFormat>
  </math>
</region>

函數 f(x, y) 是在點 (x, y) 上的密度。點與原點之間的距離是成比例的。

4. 求解已定義區域內的質量。

按一下以複製此運算式

<region id="ID0EEU4R" top="1017.6" left="19.2" xml:lang="zh_TW" height="56.8" width="178.191666666667" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="166" xml:lang="zh_TW">
    <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">
      <id xml:space="preserve" xml:lang="zh_TW" label="None">mass</id>
      <apply xml:lang="zh_TW">
        <integral xml:lang="zh_TW" />
        <lambda xml:lang="zh_TW">
          <boundVars xml:lang="zh_TW">
            <id xml:space="preserve" xml:lang="zh_TW">x</id>
          </boundVars>
          <apply xml:lang="zh_TW">
            <integral xml:lang="zh_TW" />
            <lambda xml:lang="zh_TW">
              <boundVars xml:lang="zh_TW">
                <id xml:space="preserve" xml:lang="zh_TW">y</id>
              </boundVars>
              <apply xml:lang="zh_TW">
                <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">f</id>
                <sequence xml:lang="zh_TW">
                  <id xml:space="preserve" xml:lang="zh_TW">x</id>
                  <id xml:space="preserve" xml:lang="zh_TW">y</id>
                </sequence>
              </apply>
            </lambda>
            <lowerBound xml:lang="zh_TW">
              <real xml:lang="zh_TW">-0.5</real>
            </lowerBound>
            <upperBound xml:lang="zh_TW">
              <id xml:space="preserve" xml:lang="zh_TW">x</id>
            </upperBound>
          </apply>
        </lambda>
        <lowerBound xml:lang="zh_TW">
          <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">a</id>
        </lowerBound>
        <upperBound xml:lang="zh_TW">
          <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">b</id>
        </upperBound>
      </apply>
    </define>
    <resultFormat xml:lang="zh_TW">
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" />
    </resultFormat>
  </math>
</region>

按一下以複製此運算式

5. 尋找質量CoM中心的位置。

按一下以複製此運算式

<region id="ID0EQW4R" top="1190.4" left="19.2" xml:lang="zh_TW" height="56.8" width="256.548333333333" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="168" xml:lang="zh_TW">
    <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">
      <id xml:space="preserve" xml:lang="zh_TW" label="None">X_com</id>
      <apply xml:lang="zh_TW">
        <mult xml:lang="zh_TW" />
        <apply xml:lang="zh_TW">
          <div xml:lang="zh_TW" />
          <real xml:lang="zh_TW">1</real>
          <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">mass</id>
        </apply>
        <apply xml:lang="zh_TW">
          <integral xml:lang="zh_TW" />
          <lambda xml:lang="zh_TW">
            <boundVars xml:lang="zh_TW">
              <id xml:space="preserve" xml:lang="zh_TW">x</id>
            </boundVars>
            <apply xml:lang="zh_TW">
              <integral xml:lang="zh_TW" />
              <lambda xml:lang="zh_TW">
                <boundVars xml:lang="zh_TW">
                  <id xml:space="preserve" xml:lang="zh_TW">y</id>
                </boundVars>
                <apply xml:lang="zh_TW">
                  <mult xml:lang="zh_TW" />
                  <id xml:space="preserve" xml:lang="zh_TW">x</id>
                  <apply xml:lang="zh_TW">
                    <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">f</id>
                    <sequence xml:lang="zh_TW">
                      <id xml:space="preserve" xml:lang="zh_TW">x</id>
                      <id xml:space="preserve" xml:lang="zh_TW">y</id>
                    </sequence>
                  </apply>
                </apply>
              </lambda>
              <lowerBound xml:lang="zh_TW">
                <real xml:lang="zh_TW">-0.5</real>
              </lowerBound>
              <upperBound xml:lang="zh_TW">
                <id xml:space="preserve" xml:lang="zh_TW">x</id>
              </upperBound>
            </apply>
          </lambda>
          <lowerBound xml:lang="zh_TW">
            <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">a</id>
          </lowerBound>
          <upperBound xml:lang="zh_TW">
            <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">b</id>
          </upperBound>
        </apply>
      </apply>
    </define>
    <resultFormat xml:lang="zh_TW">
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" />
    </resultFormat>
  </math>
</region>

按一下以複製此運算式

<region id="ID0ECX4R" top="1267.2" left="19.2" xml:lang="zh_TW" height="56.8" width="255.725" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="169" xml:lang="zh_TW">
    <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">
      <id xml:space="preserve" xml:lang="zh_TW" label="None">Y_com</id>
      <apply xml:lang="zh_TW">
        <mult xml:lang="zh_TW" />
        <apply xml:lang="zh_TW">
          <div xml:lang="zh_TW" />
          <real xml:lang="zh_TW">1</real>
          <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">mass</id>
        </apply>
        <apply xml:lang="zh_TW">
          <integral xml:lang="zh_TW" />
          <lambda xml:lang="zh_TW">
            <boundVars xml:lang="zh_TW">
              <id xml:space="preserve" xml:lang="zh_TW">x</id>
            </boundVars>
            <apply xml:lang="zh_TW">
              <integral xml:lang="zh_TW" />
              <lambda xml:lang="zh_TW">
                <boundVars xml:lang="zh_TW">
                  <id xml:space="preserve" xml:lang="zh_TW">y</id>
                </boundVars>
                <apply xml:lang="zh_TW">
                  <mult xml:lang="zh_TW" />
                  <id xml:space="preserve" xml:lang="zh_TW">y</id>
                  <apply xml:lang="zh_TW">
                    <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">f</id>
                    <sequence xml:lang="zh_TW">
                      <id xml:space="preserve" xml:lang="zh_TW">x</id>
                      <id xml:space="preserve" xml:lang="zh_TW">y</id>
                    </sequence>
                  </apply>
                </apply>
              </lambda>
              <lowerBound xml:lang="zh_TW">
                <real xml:lang="zh_TW">-0.5</real>
              </lowerBound>
              <upperBound xml:lang="zh_TW">
                <id xml:space="preserve" xml:lang="zh_TW">x</id>
              </upperBound>
            </apply>
          </lambda>
          <lowerBound xml:lang="zh_TW">
            <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">a</id>
          </lowerBound>
          <upperBound xml:lang="zh_TW">
            <id xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true" label="Variable">b</id>
          </upperBound>
        </apply>
      </apply>
    </define>
    <resultFormat xml:lang="zh_TW">
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" />
    </resultFormat>
  </math>
</region>

按一下以複製此運算式

6. 顯示上一個繪圖上的 CoM

按一下以複製此運算式

<region id="ID0EJZ4R" top="1420.8" left="19.2" xml:lang="zh_TW" height="287.872906403941" width="594.910344827586" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot background-type="white" origin-positioning="false" xml:lang="zh_TW" show-axis-expressions="true">
    <xyPlot xml:lang="zh_TW">
      <title class="- topic/title " xml:lang="zh_TW" toc="yes" wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" />
      <legend xml:lang="zh_TW" />
      <traces xml:lang="zh_TW">
        <trace resultRef="171" xml:lang="zh_TW">
          <traceStyle color="#FF0000FF" symbol="none" line-weight="1" line-style="Solid" xml:lang="zh_TW">線條</traceStyle>
        </trace>
        <trace resultRef="172" xml:lang="zh_TW">
          <traceStyle color="#FF0C0C0C" symbol="none" line-weight="1" line-style="Solid" xml:lang="zh_TW">線條</traceStyle>
        </trace>
        <trace resultRef="173" xml:lang="zh_TW">
          <traceStyle color="#FF800080" symbol="none" line-weight="1" line-style="Solid" xml:lang="zh_TW">線條</traceStyle>
        </trace>
        <trace resultRef="174" xml:lang="zh_TW">
          <traceStyle color="#FF008000" symbol="none" line-weight="1" line-style="Solid" xml:lang="zh_TW">線條</traceStyle>
        </trace>
        <trace resultRef="175" xml:lang="zh_TW">
          <traceStyle color="#FFFF0000" symbol="filledStar" line-weight="1" line-style="None" xml:lang="zh_TW">線條</traceStyle>
        </trace>
      </traces>
      <graph-size width="456.510344827586" height="230.272906403941" xml:lang="zh_TW" />
      <axes xml:lang="zh_TW">
        <xAxis rank="1" legend-position="PlotBoundaryBottom" start="-0.1" end="1" xml:lang="zh_TW">
          <axisLine position="origin" positionticmark="3" legendWidth="314.36091954023" xml:lang="zh_TW" />
          <axisGrid xml:lang="zh_TW">
            <gridFrequency xml:lang="zh_TW">12</gridFrequency>
            <gridLabels display="true" xml:lang="zh_TW" />
            <gridLines xml:lang="zh_TW" />
            <tickMarks display="true" xml:lang="zh_TW" />
          </axisGrid>
          <axisLabel xml:lang="zh_TW" />
          <markers xml:lang="zh_TW" />
          <numberFormat xml:lang="zh_TW">
            <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" xml:lang="zh_TW" />
          </numberFormat>
          <plotEquations xml:lang="zh_TW">
            <plotEquation xml:lang="zh_TW">
              <math resultRef="178" xml:lang="zh_TW">
                <id xml:space="preserve" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">a</id>
              </math>
              <math resultRef="179" xml:lang="zh_TW">
                <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
            <plotEquation xml:lang="zh_TW">
              <math resultRef="180" xml:lang="zh_TW">
                <id xml:space="preserve" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">b</id>
              </math>
              <math resultRef="181" xml:lang="zh_TW">
                <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
            <plotEquation xml:lang="zh_TW">
              <math resultRef="182" xml:lang="zh_TW">
                <id xml:space="preserve" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">x</id>
              </math>
              <math resultRef="183" xml:lang="zh_TW">
                <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
            <plotEquation xml:lang="zh_TW">
              <math resultRef="184" xml:lang="zh_TW">
                <id xml:space="preserve" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">x</id>
              </math>
              <math resultRef="185" xml:lang="zh_TW">
                <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
            <plotEquation xml:lang="zh_TW">
              <math resultRef="186" xml:lang="zh_TW">
                <id xml:space="preserve" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">X_com</id>
              </math>
              <math resultRef="187" xml:lang="zh_TW">
                <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true" xml:lang="zh_TW">
            <startValue xml:lang="zh_TW" resultRef="177">
              <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">-0.1</real>
            </startValue>
            <endValue xml:lang="zh_TW">
              <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </xAxis>
        <yAxis rank="1" legend-position="PlotBoundaryLeft" start="-0.6" end="1.2" xml:lang="zh_TW">
          <axisLine position="ticknumberlock" positionticmark="0" legendWidth="99.1933333333333" xml:lang="zh_TW" />
          <axisGrid xml:lang="zh_TW">
            <gridFrequency xml:lang="zh_TW">10</gridFrequency>
            <gridLabels display="true" xml:lang="zh_TW" />
            <gridLines xml:lang="zh_TW" />
            <tickMarks display="true" xml:lang="zh_TW" />
          </axisGrid>
          <axisLabel xml:lang="zh_TW" />
          <markers xml:lang="zh_TW" />
          <numberFormat xml:lang="zh_TW">
            <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" xml:lang="zh_TW" />
          </numberFormat>
          <plotEquations xml:lang="zh_TW">
            <plotEquation xml:lang="zh_TW">
              <math resultRef="194" xml:lang="zh_TW">
                <id xml:space="preserve" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">y</id>
              </math>
              <math resultRef="195" xml:lang="zh_TW">
                <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
            <plotEquation xml:lang="zh_TW">
              <math resultRef="196" xml:lang="zh_TW">
                <id xml:space="preserve" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">z</id>
              </math>
              <math resultRef="197" xml:lang="zh_TW">
                <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
            <plotEquation xml:lang="zh_TW">
              <math resultRef="198" xml:lang="zh_TW">
                <apply xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">
                  <id xml:space="preserve" xml:lang="zh_TW">c</id>
                  <id xml:space="preserve" xml:lang="zh_TW">x</id>
                </apply>
              </math>
              <math resultRef="199" xml:lang="zh_TW">
                <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
            <plotEquation xml:lang="zh_TW">
              <math resultRef="200" xml:lang="zh_TW">
                <apply xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">
                  <id xml:space="preserve" xml:lang="zh_TW">d</id>
                  <id xml:space="preserve" xml:lang="zh_TW">x</id>
                </apply>
              </math>
              <math resultRef="201" xml:lang="zh_TW">
                <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
            <plotEquation xml:lang="zh_TW">
              <math resultRef="202" xml:lang="zh_TW">
                <id xml:space="preserve" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">Y_com</id>
              </math>
              <math resultRef="203" xml:lang="zh_TW">
                <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true" xml:lang="zh_TW">
            <startValue xml:lang="zh_TW" resultRef="189">
              <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">-0.6</real>
            </startValue>
            <secondTickValue resultRef="191" xml:lang="zh_TW">
              <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">-0.4</real>
            </secondTickValue>
            <endValue xml:lang="zh_TW" resultRef="193">
              <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">1</real>
            </endValue>
          </xyDomain>
        </yAxis>
      </axes>
    </xyPlot>
  </plot>
</region>