View of /trunk/NationalProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/10_Infinite_Series/10.1_Sequences/10.1.3.pg

    1 ## DBsubject('Calculus')
    2 ## DBchapter('Limits and Derivatives')
    3 ## DBsection('Definition of the Derivative')
    4 ## KEYWORDS('calculus', 'derivatives', 'slope')
    5 ## TitleText1('Calculus: Early Transcendentals')
    6 ## EditionText1('2')
    7 ## AuthorText1('Rogawski')
    8 ## Section1('10.1')
    9 ## Problem1('3')
   10 ## Author('Keith Thompson')
   11 ## Institution('W.H.Freeman')
   12 
   13 DOCUMENT();
   14 loadMacros("PG.pl","PGbasicmacros.pl","PGanswermacros.pl");
   15 loadMacros("Parser.pl");
   16 loadMacros("freemanMacros.pl");
   17 #loadMacros("PGauxiliaryFunctions.pl");
   18 #loadMacros("PGgraphmacros.pl");
   19 
   20 #$showPartialCorrectAnswers=1;
   21 $base=Real(random(2,4,1));
   22 $a = Real(random(2,9,1));
   23 
   24 Context()->variables->add(n=>'Real');
   25 $fn = Formula("$a * $base^n/n!"); #added LAD
   26 
   27 $c1 = $fn->eval(n=>1);
   28 $c2 = $fn->eval(n=>2);
   29 $c3 = $fn->eval(n=>3);
   30 $c4 = $fn->eval(n=>4);
   31 Context()->flags->set(reduceConstants=>0);
   32 $c1sol = $fn->substitute(n=>1);
   33 $c2sol = $fn->substitute(n=>2);
   34 $c3sol = $fn->substitute(n=>3);
   35 $c4sol = $fn->substitute(n=>4);
   36 
   37 Context()->texStrings;
   38 BEGIN_TEXT
   39 \{ beginproblem() \}
   40 \{ textbook_ref_exact("Rogawski ET 2e", "10.1","3") \}
   41 $PAR
   42 Calculate the first four terms of the following sequence, starting with \(n=1\).
   43 \[ c_n=$fn\]
   44 $BR \(c_1\) =  \{ans_rule()\}
   45 $BR \(c_2\) =  \{ans_rule()\}
   46 $BR \(c_3\) =  \{ans_rule()\}
   47 $BR \(c_4\) =  \{ans_rule()\}
   48 END_TEXT
   49 
   50 Context()->normalStrings;
   51 
   52 ANS($c1->cmp);
   53 ANS($c2->cmp);
   54 ANS($c3->cmp);
   55 ANS($c4->cmp);
   56 Context()->texStrings;
   57 SOLUTION(EV3(<<'END_SOLUTION'));
   58 $PAR
   59 $SOL
   60 Setting \(n=1,2,3,4\) in the formula for \(c_n\) gives
   61 \[c_1=$c1sol = $c1,\qquad c_2=$c2sol=$c2\]
   62 \[c_3=$c3sol \approx $c3, \qquad c_4=$c4sol \approx $c4\].
   63 END_SOLUTION
   64 
   65 ENDDOCUMENT();