Limit Operator

Operators > Symbolic Operators > Limit Operator

Limit Operator

Operator	Description	Keyboard Shortcut
	Evaluates the limit of a symbolic expression.	Ctrl+L

The limit operator contains four placeholders:

1. Left-side of arrow—Limiting variable

2. Right-side of arrow—Limiting value

3. Limit Side

◦ Right-hand (+)

◦ Left-hand (-)

◦ Two-sided (empty)

4. Expression—Expression for which you want to compute the limit.

When using the limit operator and specifying the limit value:

• PTC Mathcad treats unsigned infinity the same way it treats positive infinity for functions of real variables.

• The limit value placeholder allows the insertion of ∞ and -∞, but not +∞. This reinforces the statement that PTC Mathcad treats +∞ and ∞ as equals.

Examples

<region id="ID0ENT4R" actualWidth="138.645" actualHeight="61.241333333333337" top="57.600000000000009" left="19.200000000000003" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="2">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <limit />
        <lambda>
          <boundVars>
            <id xml:space="preserve">n</id>
          </boundVars>
          <apply>
            <pow />
            <parens>
              <apply>
                <plus />
                <real>1</real>
                <apply>
                  <div />
                  <real>1</real>
                  <id xml:space="preserve">n</id>
                </apply>
              </apply>
            </parens>
            <id xml:space="preserve">n</id>
          </apply>
        </lambda>
        <id xml:space="preserve" labels="CONSTANT">∞</id>
      </apply>
      <command>
        <placeholder />
      </command>
      <symResult>
        <id xml:space="preserve" labels="CONSTANT">e</id>
      </symResult>
    </symEval>
  </math>
</region>

<region id="ID0EGU4R" actualWidth="121.78166666666668" actualHeight="56.800000000000004" top="153.60000000000002" left="19.200000000000003" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="3">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <limit />
        <lambda>
          <boundVars>
            <id xml:space="preserve">x</id>
          </boundVars>
          <apply>
            <div />
            <apply>
              <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">sin</id>
              <id xml:space="preserve">x</id>
            </apply>
            <id xml:space="preserve">x</id>
          </apply>
        </lambda>
        <real>0</real>
      </apply>
      <command>
        <placeholder />
      </command>
      <symResult>
        <real>1</real>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

Additional Information

• You cannot evaluate limits using the numerical equal sign =.

• If the limit does not exist, PTC Mathcad returns an error message.

Related Topics

About Symbolic Calculus

Symbolic Evaluation Operator

Evaluation Operator

Example: Symbolic Calculus I

Example: Symbolic Calculus II

Example: Using the Limit Operator

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