DifferentiateFunction1
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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 |
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Problem tagging: |
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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: |