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| 1 : | aubreyja | 2584 | ## 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('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 : | #add variation, LAD | ||
| 22 : | $c = Real(random(2,9,1)); | ||
| 23 : | |||
| 24 : | $ans1=$c*(5/4); | ||
| 25 : | $ans2=$c*205/144; | ||
| 26 : | $ans3=$c*5369/3600; | ||
| 27 : | Context()->texStrings; | ||
| 28 : | BEGIN_TEXT | ||
| 29 : | \{ beginproblem() \} | ||
| 30 : | \{ textbook_ref_exact("Rogawski ET 2e", "10.2","3") \} | ||
| 31 : | $PAR | ||
| 32 : | |||
| 33 : | Compute the partial sums \(S_2,S_4\), and \(S_6\). | ||
| 34 : | \[$c+\frac{$c}{2^2}+\frac{$c}{3^2}+\frac{$c}{4^2}+\cdots\] | ||
| 35 : | |||
| 36 : | |||
| 37 : | $PAR \(S_2\) = \{ans_rule()\} | ||
| 38 : | $PAR \(S_4\) = \{ans_rule()\} | ||
| 39 : | $PAR \(S_6\) = \{ans_rule()\} | ||
| 40 : | END_TEXT | ||
| 41 : | |||
| 42 : | Context()->normalStrings; | ||
| 43 : | |||
| 44 : | ANS(Real($ans1)->cmp); | ||
| 45 : | ANS(Real($ans2)->cmp); | ||
| 46 : | ANS(Real($ans3)->cmp); | ||
| 47 : | |||
| 48 : | Context()->texStrings; | ||
| 49 : | SOLUTION(EV3(<<'END_SOLUTION')); | ||
| 50 : | $PAR | ||
| 51 : | $SOL | ||
| 52 : | \(S_2=$c+\frac{$c}{2^2}=$c\left( 1+\frac{1}{4}\right)=$c\left(\frac{5}{4}\right)\); | ||
| 53 : | $PAR | ||
| 54 : | \(S_4=$c+\frac{$c}{2^2}+\frac{$c}{3^2}+\frac{$c}{4^2}=$c\left(\frac{205}{144}\right)\); | ||
| 55 : | $PAR | ||
| 56 : | \(S_6=$c+\frac{$c}{2^2}+\frac{$c}{3^2}+\frac{$c}{4^2}+\frac{$c}{5^2}+\frac{$c}{6^2}=$c\left(\frac{5369}{3600}\right)\). | ||
| 57 : | |||
| 58 : | END_SOLUTION | ||
| 59 : | |||
| 60 : | ENDDOCUMENT(); |
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