## WeBWorK Problems

### Can't generate enough valid points for comparison ### Can't generate enough valid points for comparison

by Bill Shillito -
Number of replies: 2

Hello! I'm having some trouble with a WebWork question I authored. It seems that whenever $a is between 2 and 7, the problem works fine, but when$a is 8 or greater, it gives the error "Can't generate enough valid points for comparison". I've set the domain to [$a+1,$a+10], so I know the function should be defined on this interval (since it's defined from -∞ to -$a and from$a to +∞).

########################################################################DOCUMENT();      loadMacros(   "PGstandard.pl",     # Standard macros for PG language   "MathObjects.pl",   "contextFraction.pl",   "PGML.pl",   "scaffold.pl",      "PGchoicemacros.pl",   "PGstandard.pl","PGunion.pl","PGnumericalmacros.pl","PGstatisticsmacros.pl","MathObjects.pl","parserPopUp.pl","PGML.pl","unionTables.pl","niceTables.pl","PGcourse.pl","PGchoicemacros.pl","answerHints.pl","weightedGrader.pl","parserRadioButtons.pl","parserNumberWithUnits.pl","randomizers.pl","AnswerFormatHelp.pl","parserFormulaUpToConstant.pl");#### Example of a question with numeric values as the answers.### Question involving Functions# Create a random function$a = random(2,13);$asq = $a**2;$b = 5;Context()->variables->set(x => {limits => [a+1,a+10]});$f = Formula("1/(x*sqrt(x^2-$a^2))")->reduce();#FormulaUpToConstant is used for antiderivatives - this allows the student to use any integration constant (C, K, etc)$antiderivative = FormulaUpToConstant("1/$a * asec(x/$a)");$adwoc = FormulaUpToConstant("asec(x/$a)");BEGIN_PGMLCalculate [\int[$f]\,\mathrm dx].(Hint: Make the substitution [x=[$a]u].)[_]{$antiderivative} [@ AnswerFormatHelp("formulas") @]*END_PGMLBEGIN_PGML_SOLUTIONMake the substitution [x=[$a]u] as suggested, which means [x^2=[$asq]u^2] and [\mathrm dx=[$a]\,\mathrm du].Simplify after making the substitution, pulling the [[$a]] out of the square root.You should find you have an extra factor of [[$a]] on the bottom.The answer is [\dfrac1{[$a]}[\$adwoc]].END_PGML_SOLUTIONENDDOCUMENT(); ### Re: Can't generate enough valid points for comparison

by Danny Glin -

In your code you are missing the dollar signs on a+1 and a+10. 