Shows how to test a formula at a given set of points.
Download file: FormulaTestPoints.pg
DOCUMENT();
loadMacros('PGstandard.pl', 'PGML.pl', 'PGcourse.pl');
Preamble
These standard macros need to be loaded.Context()->variables->set(x => { limits => [ -1, 1 ] });
$f = Compute('sqrt(x + 1)');
$g = Compute('sqrt(x^2 - 4)');
$g->{test_points} = [ [-3], [-2], [2], [3], [4] ];
Setup
The first line sets the limits of evaluation for the variable
x and for any answer in the context to
[-1, 1].
Alternatively, the limits for all variables in the context can be set
with Context()->flags->set(limits => [-1, 1]).
For another alternative, the limits for the context could be left at
their default values, and instead the limits for a specific formula can
be set with $f->{limits} = [-1, 1].
For the test points of $g, note that the domain of
$g is (-inf, -2] U [2,inf). One way to handle
this would be to set the limits for the function to be some
interval contained in the domain. Alternatively, as shown, the test
points can be set with the test_points field to be a
specific set of values in the domain.
BEGIN_PGML
Enter [`[$f]`]: [___]{$f}
Enter [`[$g]`]: [___]{$g}
END_PGML
Statement
This is the problem statement in PGML.BEGIN_PGML_SOLUTION Solution explanation goes here. END_PGML_SOLUTION ENDDOCUMENT();
Solution
A solution should be provided here.