View of /trunk/NationalProblemLibrary/ma122DB/set3/s2_9_39.pg

    1 ##KEYWORDS('derivatives', 'limits')
    2 ##DESCRIPTION
    3 ##  Evaluate some limits
    4 ##ENDDESCRIPTION
    5 
    6 ## Shotwell cleaned
    7 ## tcao , PAID on 11-24-2003
    8 
    9 ## DBsubject('Calculus')
   10 ## DBchapter('Limits and Derivatives')
   11 ## DBsection('The Derivative as a Function')
   12 ## Date('6/3/2002')
   13 ## Author('')
   14 ## Institution('')
   15 ## TitleText1('Calculus: Early Transcendentals')
   16 ## EditionText1('6')
   17 ## AuthorText1('Stewart')
   18 ## Section1('2.8')
   19 ## Problem1('39')
   20 
   21 DOCUMENT();        # This should be the first executable line in the problem.
   22 
   23 loadMacros(
   24 "PGbasicmacros.pl",
   25 "PGanswermacros.pl",
   26 "PGauxiliaryFunctions.pl"
   27 );
   28 
   29 TEXT(beginproblem());
   30 $showPartialCorrectAnswers = 1;
   31 
   32 $a1 = random(2,10,1);
   33 
   34 BEGIN_TEXT
   35 Let \( f(x) =  |x-$a1| \). Evaluate the following limits.
   36 $BR$BR
   37 \( \lim_{x\to $a1^-} \frac{f(x)-f($a1)}{x-$a1}= \) \{ans_rule(10) \}
   38 $BR$BR
   39 \( \lim_{x\to $a1^+} \frac{f(x)-f($a1)}{x-$a1}= \) \{ans_rule(10) \}
   40 $BR$BR
   41 Thus the function \(f(x)\) is not differentiable at $a1.
   42 END_TEXT
   43 
   44 ANS(num_cmp(-1));
   45 ANS(num_cmp(1));
   46 
   47 
   48 
   49 ENDDOCUMENT();        # This should be the last executable line in the problem.