[npl] / trunk / NationalProblemLibrary / WHFreeman / Rogawski_Calculus_Early_Transcendentals_Second_Edition / 10_Infinite_Series / 10.2_Summing_an_Infinite_Series / 10.2.25.pg Repository:
ViewVC logotype

View of /trunk/NationalProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/10_Infinite_Series/10.2_Summing_an_Infinite_Series/10.2.25.pg

Parent Directory Parent Directory | Revision Log Revision Log


Revision 2584 - (download) (annotate)
Tue Nov 8 15:17:41 2011 UTC (2 years, 5 months ago) by aubreyja
File size: 1697 byte(s)
Rogawski problems contributed by publisher WHFreeman. These are a subset of the problems available to instructors who use the Rogawski textbook. The remainder can be obtained from the publisher.

    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('10.2')
    9 ## Problem1('25')
   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 
   22 $num=random(3,7,2); #force odd
   23 $den=random(10,14,2); #force even
   24 $n0 = random(2,6,1);
   25 $den_num = $den-$num;
   26 
   27 $ans1=($num**$n0)/($den**$n0)*($den/($den-$num));
   28 Context()->texStrings;
   29 BEGIN_TEXT
   30 \{ beginproblem() \}
   31 \{ textbook_ref_exact("Rogawski ET 2e", "10.2","25") \}
   32 $PAR
   33 
   34 Use the formula for the sum of a geometric series to find the sum or state that the series diverges (enter DIV for a divergent series).
   35 
   36 \[\sum_{n=$n0}^\infty \frac{$num^n}{$den^n}\]
   37 
   38 $PAR \(S=\) \{ans_rule()\}
   39 END_TEXT
   40 
   41 Context()->normalStrings;
   42 
   43 ANS(std_num_str_cmp($ans1,['DIV']));
   44 
   45 Context()->texStrings;
   46 SOLUTION(EV3(<<'END_SOLUTION'));
   47 $PAR
   48 $SOL
   49 This is a geometric series with \(c=\left(\frac{$num}{$den}\right)^{$n0}\) and \(0<r=\frac{$num}{$den}<1\). Thus,
   50 \[\sum_{n=$n0}^\infty \frac{$num^n}{$den^n}=
   51 \left(\frac{$num}{$den}\right)^{$n0}\sum_{n=0}^\infty\left( \frac{$num}{$den}\right)^n=
   52 \left(\frac{$num}{$den}\right)^{$n0}\left(\frac{1}{1-\frac{$num}{$den}}\right)=\left(\frac{$num}{$den}\right)^{$n0}\left(\frac{$den}{$den_num}\right).\]
   53 END_SOLUTION
   54 ENDDOCUMENT();

aubreyja at gmail dot com
ViewVC Help
Powered by ViewVC 1.0.9