RecursivelyDefinedFunctions
Recursively Defined Functions (Sequences)
This PG code shows how to check student answers that are recursively defined functions.
PG problem file | Explanation |
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DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "parserFunction.pl", ); TEXT(beginproblem()); |
Initialization:
We will be defining a new named function and adding it to the context, and the easiest way to do this is using |
Context("Numeric")->variables->are(n=>"Real"); parserFunction(f => "sin(pi^n)+e"); $fn = Formula("3 f(n-1) + 2"); |
Setup:
We define a new named function |
Context()->texStrings; BEGIN_TEXT The current value \( f(n) \) is three times the previous value, plus two. Find a recursive definition for \( f(n) \). Enter \( f_{n-1} \) as \( f(n-1) \). $BR \( f(n) \) = \{ ans_rule(20) \} END_TEXT Context()->normalStrings; |
Main Text: The problem text section of the file is as we'd expect. We should tell students to use function notation rather than subscript notation so that they aren't confused about syntax. |
$showPartialCorrectAnswers=1; ANS( $fn->cmp() ); ENDDOCUMENT(); |
Answer Evaluation: As is the answer. |
- POD documentation: parserFunction.pl
- PG macro: parserFunction.pl