View of /trunk/NationalProblemLibrary/Rochester/setAlgebra28ExpFunctions/simplifying.pg

    1 ## DESCRIPTION
    2 ## Algebra: Exponential and Logarithmic Functions
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS ('exponential')
    6 ## Tagged by cmd6a 4/4/06
    7 
    8 ## DBsubject('Algebra')
    9 ## DBchapter('Exponential and Logarithmic Functions')
   10 ## DBsection('The Natural Exponential Function')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Rochester')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGauxiliaryFunctions.pl"
   28 );
   29 
   30 TEXT(beginproblem());
   31 $showPartialCorrectAnswers = 1;
   32 
   33 $a = random(-10,10,1);
   34 $b = non_zero_random(-10,10,1);
   35 $c = non_zero_random(-10,10,1);
   36 
   37 $y = random(1,10,1);
   38 $x = 2*$y;
   39 
   40 $p = random(1,10,1);
   41 $q = non_zero_random(-10,10,1);
   42 $r = random(1,10,1);
   43 $s = non_zero_random(-10,10,1);
   44 
   45 BEGIN_TEXT;
   46 Simplify the following expressions.  Give exact answers with the fewest number
   47 of \(e\)'s possible.  Then give a decimal approximation.
   48 $BR$BR
   49 (a) \[e^{$a} e^{$b} e^{$c} = \] \{ans_rule(10)\}, which is approximately
   50         \{ans_rule(10)\}.
   51 $BR$BR
   52 (b) \[\frac{e^{$x} - e^{-$x}}{e^{$y} - e^{-$y}} = \] \{ans_rule(10)\},
   53         which is approximately \{ans_rule(10)\}.
   54 $BR$BR
   55 (c) \[ (e^{$p} + $q)(e^{$r} + $s)  =\] \{ans_rule(10)\}, which is approximately
   56         \{ans_rule(10)\}
   57 
   58 END_TEXT;
   59 
   60 $exp1 = $a+$b+$c;
   61 $ans1 = "e**$exp1";
   62 $ans2 = $E**$exp1;
   63 
   64 ANS(fun_cmp($ans1,var=>['e']));
   65 ANS(num_cmp($ans2, mode=>"strict"));
   66 
   67 $ans3 = "(e**$x+1)/(e**$y)";
   68 $ans4 = ($E**$x+1)/($E**$y);
   69 
   70 ANS(fun_cmp($ans3,var=>['e']));
   71 ANS(num_cmp($ans4, mode=>"strict"));
   72 
   73 $ans5 = "e**($p+$r) + $s*e**$p + $q*e**$r +$q*$s";
   74 $ans6 = $E**($p+$r) + $s*$E**$p + $q*$E**$r+$q*$s;
   75 
   76 ANS(fun_cmp($ans5,var=>['e']));
   77 ANS(num_cmp($ans6, mode=>"strict"));
   78 ENDDOCUMENT();        # This should be the last executable line in the problem.
   79