Difference between revisions of "DifferentiateFunction1"
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(Created page with '<h2>Differentiating and Evaluating a Function</h2> 300px|thumb|right|Click to enlarge <p style="background-color:#f9f9f9;border:black solid 1…') |
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<b>Initialization:</b> |
<b>Initialization:</b> |
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| + | We load <code>unionLists.pl</code> to create an enumerated list in the Main Text section. |
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$answer[1] = $fx->substitute(k=>$k); # formula |
$answer[1] = $fx->substitute(k=>$k); # formula |
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| − | # $answer[1] = $fx->eval(k=>$k); # gives errors, must eval to real |
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$answer[2] = $fx->substitute(x=>$a*pi,k=>$k); # formula |
$answer[2] = $fx->substitute(x=>$a*pi,k=>$k); # formula |
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| − | <b>Setup:</b> |
+ | <b>Setup:</b> |
| + | The partial differentiation operator is <code>->D('x')</code>. |
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| + | </p> |
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| + | The main difference between <code>eval()</code> and <code>substitute()</code> is |
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| + | * <code>eval()</code> returns a Real (a number) |
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| + | * <code>substitute()</code> returns a Formula |
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| + | Since plugging a particular number <code>$k</code> into the Formula <code>$f</code> returns a Formula <code>$k x</code>, the eval method <code>$answer[1] = $fx->eval(k=>$k);</code> gives errors because eval returns a Real (not a Formula). The substitute method returns a Formula, so there are no errors using <code>$answer[1] = $fx->substitute(k=>$k);</code>. |
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| + | </p> |
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| + | Setting the context flag <code>reduceConstants=>1</code> would reduce answers to decimals, and setting it to zero does not evaluate to decimals. |
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Revision as of 18:26, 4 December 2010
Differentiating and Evaluating a Function
This PG code shows how to create a function using MathObjects, differentiate it, and evaluate it.
- Download file: File:DifferentiateFunction1.txt (change the file extension from txt to pg when you save it)
- File location in NPL:
FortLewis/Authoring/Templates/DiffCalc/DifferentiateFunction1.pg
| PG problem file | Explanation |
|---|---|
|
Problem tagging: |
|
DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "AnswerFormatHelp.pl", "unionLists.pl", ); TEXT(beginproblem()); |
Initialization:
We load |
Context("Numeric")->variables->add(k=>"Real");
Context()->flags->set(
reduceConstants=>0, # no decimals
reduceConstantFunctions=>1, # combine 4+5*2?
formatStudentAnswer=>'parsed', # no decimals
);
$a = random(6,9,1);
$k = random(3,5,1);
$f = Formula("k x^2");
$fx = $f->D('x');
@answer = ();
$answer[0] = $fx;
$answer[1] = $fx->substitute(k=>$k); # formula
$answer[2] = $fx->substitute(x=>$a*pi,k=>$k); # formula
#$answer[2] = $fx->eval(x=>$a*pi,k=>$k); # real
|
Setup:
The partial differentiation operator is
The main difference between
$k into the Formula $f returns a Formula $k x, the eval method $answer[1] = $fx->eval(k=>$k); gives errors because eval returns a Real (not a Formula). The substitute method returns a Formula, so there are no errors using $answer[1] = $fx->substitute(k=>$k);.
Setting the context flag |
Context()->texStrings;
BEGIN_TEXT
Suppose \( f(x) = $f \) where \( k \) is a
constant.
\{ BeginList("OL",type=>"a") \}
$ITEM \( f'(x) = \)
\{ ans_rule(20) \}
\{ AnswerFormatHelp("formulas") \}
$ITEM If \( k = $k \) then \( f'(x) = \)
\{ ans_rule(20) \}
\{ AnswerFormatHelp("formulas") \}
$ITEM If \( k = $k \) then \( f'($a\pi) = \)
\{ ans_rule(20) \}
\{ AnswerFormatHelp("formulas") \}
\{ EndList("OL") \}
END_TEXT
Context()->normalStrings;
|
Main Text: |
$showPartialCorrectAnswers = 1;
foreach my $i (0..2) {
ANS( $answer[$i]->cmp() );
}
|
Answer Evaluation: |
Context()->texStrings;
BEGIN_SOLUTION
${PAR}SOLUTION:${PAR}
Solution explanation goes here.
END_SOLUTION
Context()->normalStrings;
COMMENT("MathObject version.");
ENDDOCUMENT();
|
Solution: |
