Schlüsselwort "standard" verwenden

Symbolische Mathematik > Arbeiten mit symbolischer Mathematik > Schlüsselwort "standard" verwenden

Verwenden Sie das Schlüsselwort standard, um die Berechnungsergebnisse in einem Standardformat zu erhalten. Das Schlüsselwort standard ist insbesondere für Integrale und Reihenentwicklungen vorgesehen. In den nachfolgenden Beispielen finden Sie verschiedene Anwendungsfälle.

Symbolische Integralfunktionen

Verwenden Sie das Schlüsselwort standard, um das Integrationsergebnis mit der Integrationskonstanten _C1 zu erhalten.

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        <command>
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        <symResult>
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              <neg />
              <apply>
                <id labels="FUNCTION" xml:space="preserve">cos</id>
                <id labels="VARIABLE" xml:space="preserve">x</id>
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            <id labels="VARIABLE" xml:space="preserve">_C1</id>
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Sie können der Integralkonstanten einen Wert zuweisen:

1. Legen Sie den Wert der Integralkonstanten fest.

2. Geben Sie die Integralfunktion ein.

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            <plus />
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              <neg />
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                <id labels="FUNCTION" xml:space="preserve">cos</id>
                <id labels="VARIABLE" xml:space="preserve">x</id>
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            <id labels="VARIABLE" xml:space="preserve">_C1</id>
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3. Plotten Sie die Integralfunktion.

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4. Vergleichen Sie die geplottete Funktion mit der gleichen Funktion ohne Integralkonstanten. Wie Sie sehen, wird der Plot entsprechend dem Wert der Integralkonstanten verschoben.

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5. Erstellen Sie einen dreidimensionalen Plot mit allen möglichen Lösungen dieser Integralfunktion.

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    </resultFormat>
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Wenn Ihre Berechnung mehrere Integralfunktionen enthält, erhalten Sie mehr als eine Integralkonstante.

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              <real>2</real>
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            <apply>
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              <id labels="VARIABLE" xml:space="preserve">x</id>
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Reihenentwicklungen

Verwenden Sie das Schlüsselwort standard, um die O-Notation auf eine Reihenentwicklung anzuwenden. Mit der O-Notation wird der Fehlerausdruck in der Näherung der Reihenentwicklung beschrieben.

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                    <real>1</real>
                    <id labels="VARIABLE" xml:space="preserve">x</id>
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                  <apply>
                    <mult />
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                      <real>1</real>
                      <real>2</real>
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                    <apply>
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                      <real>2</real>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <mult />
                  <apply>
                    <div />
                    <real>1</real>
                    <real>6</real>
                  </apply>
                  <apply>
                    <pow />
                    <id labels="VARIABLE" xml:space="preserve">x</id>
                    <real>3</real>
                  </apply>
                </apply>
              </apply>
              <apply>
                <mult />
                <apply>
                  <div />
                  <real>1</real>
                  <real>24</real>
                </apply>
                <apply>
                  <pow />
                  <id labels="VARIABLE" xml:space="preserve">x</id>
                  <real>4</real>
                </apply>
              </apply>
            </apply>
            <apply>
              <mult />
              <apply>
                <div />
                <real>1</real>
                <real>120</real>
              </apply>
              <apply>
                <pow />
                <id labels="VARIABLE" xml:space="preserve">x</id>
                <real>5</real>
              </apply>
            </apply>
          </apply>
          <apply>
            <id labels="*" xml:space="preserve">O</id>
            <apply>
              <pow />
              <id labels="VARIABLE" xml:space="preserve">x</id>
              <real>6</real>
            </apply>
          </apply>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
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• Sie können angeben, wie viele Ausdrücke die Reihenentwicklung zurückgeben soll. Geben Sie ein Komma nach dem Schlüsselwort series ein, und fügen Sie eine positive Ganzzahl und ein weiteres Komma vor dem Schlüsselwort standard hinzu.

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          <apply>
            <id labels="*" xml:space="preserve">O</id>
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              <id labels="VARIABLE" xml:space="preserve">x</id>
              <real>2</real>
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• Wenn Sie einen Ausdruck um einen anderen Punkt als 0 erweitern möchten, geben Sie nach dem Schlüsselwort series einen Wert für die Variable ein, und verwenden Sie dabei den booleschen Gleichheitsoperator.

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                <pow />
                <id labels="CONSTANT" xml:space="preserve">e</id>
                <real>2</real>
              </apply>
              <parens>
                <apply>
                  <minus />
                  <id labels="VARIABLE" xml:space="preserve">x</id>
                  <real>2</real>
                </apply>
              </parens>
            </apply>
          </apply>
          <apply>
            <id labels="*" xml:space="preserve">O</id>
            <apply>
              <pow />
              <parens>
                <apply>
                  <minus />
                  <id labels="VARIABLE" xml:space="preserve">x</id>
                  <real>2</real>
                </apply>
              </parens>
              <real>2</real>
            </apply>
          </apply>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
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</region>

• Weisen Sie die Reihenentwicklung einer Variablen zu, und führen Sie algebraische Berechnungen durch.

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              <id labels="*" xml:space="preserve">O</id>
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              <id xml:space="preserve">series</id>
              <real>4</real>
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            <id xml:space="preserve">standard</id>
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              <id labels="VARIABLE" xml:space="preserve">x</id>
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                  <real>1</real>
                  <real>6</real>
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                  <pow />
                  <id labels="VARIABLE" xml:space="preserve">x</id>
                  <real>3</real>
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            <apply>
              <id labels="*" xml:space="preserve">O</id>
              <apply>
                <pow />
                <id labels="VARIABLE" xml:space="preserve">x</id>
                <real>5</real>
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    </define>
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  </math>
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              <real>1</real>
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            <id xml:space="preserve">standard</id>
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            <real>1</real>
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