Linear Approximation

Linear approximation

Complete Code

POD for Macro Files

PG problem file

Explanation

DOCUMENT();

loadMacros(
    'PGstandard.pl',  'PGML.pl',
    'answerHints.pl', 'parserAssignment.pl',
    'PGcourse.pl'
);

Preamble

We load parserAssignment.pl to require students to enter their answer as an equation of the form y = ... We load answerHints.pl to provide customized answer hints, particularly for those students who enter the slope of the line instead of the equation of the line.

Context()->variables->add(y => 'Real');
parser::Assignment->Allow;

$a  = random(2, 5);
$aa = $a**2;
$a2 = 2 * $a;

$f = Compute('sqrt(x)');

$answer = Compute("y = $a + (1/$a2) * (x-$aa)");
$cmp    = $answer->cmp()->withPostFilter(AnswerHints(
    [ Formula("1/$a2"), Formula("y=1/$a2") ] => [
        'Your answer should be an equation for a non-horizontal line.',
        replaceMessage => 1
    ],
));

Setup

We have to tell the context that we are allowing the assignment of a variable to a formula.

We use answer hints to remind students to enter an equation for a line, not just the slope of the line.

BEGIN_PGML
Find the linear approximation to [`f(x) = [$f]`] at [`x = [$aa]`].  Your
answer should be an equation in the variables [`x`] and [`y`].

[_]{$cmp}{10}
END_PGML

Statement

The variable $cmp is used in the answer blank, which call the compare method define in the setup section.

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.