Difference between revisions of "DifferenceQuotients"
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(New page: <h2>Difference Quotients as Student Answers</h2> <!-- Header for these sections -- no modification needed --> <p style="background-color:#eeeeee;border:black solid 1px;padding:3px;"> ...) |
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| − | <h2>Difference Quotients as Student Answers</h2> |
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| + | #REDIRECT [[DifferenceQuotient1]] |
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| − | <!-- Header for these sections -- no modification needed --> |
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| − | <p style="background-color:#eeeeee;border:black solid 1px;padding:3px;"> |
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| − | <em>This PG code shows how to check student answers that fully reduced difference quotients for limits that compute derivatives.</em> |
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| − | </p> |
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| − | <p style="text-align:center;"> |
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| − | [[IndexOfProblemTechniques|Problem Techniques Index]] |
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| − | </p> |
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| − | |||
| − | <table cellspacing="0" cellpadding="2" border="0"> |
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| − | |||
| − | <tr valign="top"> |
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| − | <th> PG problem file </th> |
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| − | <th> Explanation </th> |
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| − | </tr> |
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| − | <!-- Load specialized macro files section --> |
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| − | <tr valign="top"> |
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| − | <td style="background-color:#ddffdd;border:black 1px dashed;"> |
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| − | <pre> |
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| − | DOCUMENT(); |
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| − | |||
| − | loadMacros( |
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| − | "PGstandard.pl", |
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| − | "MathObjects.pl", |
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| − | "parserDifferenceQuotient.pl", |
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| − | ); |
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| − | TEXT(beginproblem()); |
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| − | </pre> |
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| − | </td> |
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| − | <td style="background-color:#ccffcc;padding:7px;"> |
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| − | <p> |
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| − | <b>Initialization:</b> |
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| − | We need to include the macros file <code>parserDifferenceQuotient.pl</code>. |
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| − | </p> |
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| − | </td> |
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| − | </tr> |
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| − | |||
| − | <!-- Setup section --> |
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| − | <tr valign="top"> |
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| − | <td style="background-color:#ffffdd;border:black 1px dashed;"> |
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| − | <pre> |
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| − | Context("Numeric"); |
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| − | $limit = DifferenceQuotient("2*x+h","h"); |
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| − | $fp = Compute("2 x"); |
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| − | </pre> |
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| − | </td> |
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| − | <td style="background-color:#ffffcc;padding:7px;"> |
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| − | <p> |
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| − | <b>Setup:</b> |
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| − | The routine <code>DifferenceQuotient("function","variable")</code> takes the simplified function and a variable name. If the variable is omitted, <code>dx</code> is used by default. |
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| − | </p> |
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| − | <p> |
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| − | If the student enters an unsimplified answer such as |
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| − | <code>((x+h)^2-x^2)/h</code>, their answer will not be marked correct and they will receive the message |
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| − | <i>It looks like you didn't finish simplifying your answer</i>. |
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| − | </p> |
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| − | |||
| − | </td> |
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| − | </tr> |
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| − | |||
| − | <!-- Question text section --> |
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| − | |||
| − | <tr valign="top"> |
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| − | <td style="background-color:#ffdddd;border:black 1px dashed;"> |
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| − | <pre> |
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| − | Context()->texStrings; |
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| − | BEGIN_TEXT |
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| − | Simplify and then evaluate the limit. |
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| − | $BR |
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| − | $BR |
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| − | \( \displaystyle |
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| − | \frac{d}{dx} \big( x^2 \big) |
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| − | = |
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| − | \lim_{h \to 0} \frac{(x+h)^2-x^2}{h} |
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| − | = |
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| − | \lim_{h \to 0} |
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| − | \big( |
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| − | \) |
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| − | \{ ans_rule(15) \} |
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| − | \( \big) = \) |
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| − | \{ ans_rule(15) \} |
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| − | END_TEXT |
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| − | Context()->normalStrings; |
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| − | </pre> |
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| − | <td style="background-color:#ffcccc;padding:7px;"> |
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| − | <p> |
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| − | <b>Main Text:</b> |
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| − | The problem text section of the file is as we'd expect. |
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| − | </p> |
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| − | </td> |
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| − | </tr> |
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| − | |||
| − | <!-- Answer section --> |
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| − | |||
| − | <tr valign="top"> |
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| − | <td style="background-color:#eeddff;border:black 1px dashed;"> |
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| − | <pre> |
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| − | $showPartialCorrectAnswers = 1; |
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| − | $showPartialCorrectAnswers = 1; |
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| − | ANS( $limit->cmp() ); |
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| − | ANS( $fp->cmp() ); |
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| − | |||
| − | ENDDOCUMENT(); |
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| − | </pre> |
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| − | <td style="background-color:#eeccff;padding:7px;"> |
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| − | <p> |
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| − | <b>Answer Evaluation:</b> |
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| − | As is the answer. |
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| − | </p> |
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| − | </td> |
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| − | </tr> |
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| − | </table> |
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| − | |||
| − | <p style="text-align:center;"> |
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| − | [[IndexOfProblemTechniques|Problem Techniques Index]] |
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| − | </p> |
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| − | |||
| − | [[Category:Problem Techniques]] |
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Latest revision as of 13:12, 22 June 2015
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