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Revision 2584 - (download) (annotate)
Tue Nov 8 15:17:41 2011 UTC (2 years, 5 months ago) by aubreyja
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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('36')
   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 Context()->variables->add(D=>'Real');
   23 $num=random(4,9);
   24 $den=$num+1;
   25 $ans1=$num**3/($den-$num);
   26 $n2=$num**2;
   27 $n3=$num**3;
   28 $d2=$den**2;
   29 $d3=$den**3;
   30 $ans1=$d3/($n2*($den-$num));
   31 Context()->texStrings;
   32 
   33 BEGIN_TEXT
   34 \{ beginproblem() \}
   35 \{ textbook_ref_exact("Rogawski ET 2e", "10.2","36") \}
   36 $PAR
   37 
   38 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).
   39 
   40 
   41 \[\frac{$d2}{$n2}+\frac{$den}{$num}+1+\frac{$num}{$den}+\frac{$n2}{$d2}+\frac{$n3}{$d3}+\cdots\]
   42 
   43 \(S=\)  \{ans_rule()\}
   44 END_TEXT
   45 
   46 Context()->normalStrings;
   47 
   48 ANS(std_num_str_cmp($ans1,['DIV']));
   49 
   50 Context()->texStrings;
   51 SOLUTION(EV3(<<'END_SOLUTION'));
   52 $PAR
   53 $SOL
   54 This is a geometric series with \(c=\left(\frac{$num}{$den}\right)^{-2}=\frac{$d2}{$n2}\) and \(0<r=\frac{$num}{$den}<1\). Thus,
   55 \[\sum_{n=0}^\infty \frac{$d2}{$n2}\left(\frac{$num}{$den}\right)^n=\frac{$d2}{$n2}\left(\frac{1}{1-\frac{$num}{$den}}\right)=\frac{$d3}{$n2($den-$num)}.\]
   56 END_SOLUTION
   57 ENDDOCUMENT();

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