text: #Problem APEX 6.7.12
  
  DOCUMENT();
  
  # Load whatever macros you need for the problem
  loadMacros(
    "PGstandard.pl",
    "MathObjects.pl",
    "PGcourse.pl"
  );
  
  ## DBsubject(Calculus - single variable)
  ## DBchapter(Applications of differentiation)
  ## DBsection(Indeterminate forms and L'Hopital's rule)
  ## Institution(Valdosta State University)
  ## Author(S. V. Ault)
  ## Level(3)
  ## MO(1)
  ## TitleText1('APEX Calculus')
  ## AuthorText1('Hartman')
  ## EditionText1('3.0')
  ## Section1('6.7')
  ## Problem1('12')
  
  $showPartialCorrectAnswers = 1;
  $a=random(2,15,1);
  
  $c = "0";
  
  $num = "\sin($a x)";
  $den = "x";
  
  $dnum = "$a \cos($a x)";
  $dden = "1";
  
  $ans = $a;
  
  TEXT(beginproblem());
  
  BEGIN_TEXT
  Evaluate the limit, using L'H\{ MODES(HTML=>"&ocirc;",TeX=>"\^o") \}pital's Rule.
  $BR
  Enter $BBOLD INF $EBOLD for \(\infty\), $BBOLD -INF $EBOLD 
  for \(-\infty\), or $BBOLD DNE $EBOLD if the limit does not exist,
  but is neither \(\infty\) nor \(-\infty\).$PAR
  \(\displaystyle \lim_{x\to $c} \frac{$num}{$den} =\)
  \{ans_rule(10) \}
  END_TEXT
  
  ANS(Compute($ans)->cmp());
  
  BEGIN_SOLUTION
  \[ 
    \lim_{x \to $c} \frac{$num}{$den}
    = \lim_{x \to $c} \frac{$dnum}{$dden}
    = $a(1) = $ans
  \]
  END_SOLUTION
  
  ENDDOCUMENT();    
  