View of /trunk/NationalProblemLibrary/270/setLimitsRates5Continuity/ur_lr_5_1.pg

    1 ## DESCRIPTION
    2 ##   Removable Discontinuity
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Discontinuity', 'Removable')
    6 ## Tagged by nhamblet
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Limits and Derivatives')
   10 ## DBsection('Continuity')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('ASU')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 ## TitleText2('Calculus: Early Transcendentals')
   20 ## EditionText2('1')
   21 ## AuthorText2('Rogawski')
   22 ## Section2('2.4')
   23 ## Problem2('23')
   24 
   25 DOCUMENT();        # This should be the first executable line in the problem.
   26 
   27 loadMacros(
   28 "PG.pl",
   29 "PGbasicmacros.pl",
   30 "PGchoicemacros.pl",
   31 "PGanswermacros.pl",
   32 "PGauxiliaryFunctions.pl"
   33 );
   34 
   35 TEXT(beginproblem());
   36 $showPartialCorrectAnswers = 1;
   37 
   38 $a = random(1,5,1);
   39 $b = random(2*$a+2,2*$a+6,1);
   40 $b2 = $b-2*$a;
   41 $ab = $a*$b;
   42 
   43 TEXT(EV2(<<EOT));
   44 $BR
   45 A function \( f(x) \) is said to have a $BBOLD removable $EBOLD discontinuity at \( x=a \) if:
   46 $BR
   47 $BBOLD 1.$EBOLD  \( f \) is either not defined or not continuous at \( x=a \). $BR
   48 $BBOLD 2.$EBOLD \( f(a) \) could either be defined or redefined so that the new function IS continuous at \(x=a\).
   49 $HR
   50 Let \( f(x) =\frac{2x^2+$b2 x -$ab}{x-$a} \)
   51 $BR
   52 Show that \( f(x) \) has a removable discontinuity at \( x=$a \) and determine what value for \( f($a) \) would make \( f(x) \) continuous at \( x=$a \).
   53 $BR
   54 Must define \( f($a)= \)\{ans_rule(15)\}.
   55 $BR
   56 EOT
   57 
   58 $ans = 2*$a+$b;
   59 ANS(num_cmp($ans));
   60 
   61 ENDDOCUMENT();        # This should be the last executable line in the problem.
   62