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| 1 : | jj | 141 | #DESCRIPTION |
| 2 : | #Taylor_series | ||
| 3 : | #ENDDESCRIPTION | ||
| 4 : | |||
| 5 : | #KEYWORDS('Taylor Series') | ||
| 6 : | |||
| 7 : | DOCUMENT(); # This should be the first executable line in the problem. | ||
| 8 : | |||
| 9 : | loadMacros( | ||
| 10 : | "PG.pl", | ||
| 11 : | "PGbasicmacros.pl", | ||
| 12 : | "PGchoicemacros.pl", | ||
| 13 : | "PGanswermacros.pl", | ||
| 14 : | "PGauxiliaryFunctions.pl" | ||
| 15 : | ); | ||
| 16 : | |||
| 17 : | TEXT(beginproblem()); | ||
| 18 : | $showPartialCorrectAnswers = 0; | ||
| 19 : | |||
| 20 : | $a = random(2,11,1); | ||
| 21 : | $b = random(2,11,1); | ||
| 22 : | $a1 =2*($a); | ||
| 23 : | |||
| 24 : | $questStr1 = EV2( " \( \displaystyle \sum_{n=0}^\infty (-1)^n | ||
| 25 : | \frac{2x^{2n+1}}{(2n+1)!} \) " ); | ||
| 26 : | |||
| 27 : | $ansStr1 =EV2( " \( 2 \sin(x) \) " ); | ||
| 28 : | |||
| 29 : | $questStr2 = EV2( " \( \displaystyle \sum_{n=0}^\infty \frac{2^n x^n}{n!} \) " ); | ||
| 30 : | |||
| 31 : | $ansStr2 =EV2( " \( e^{2x} \) " ); | ||
| 32 : | |||
| 33 : | $questStr3 = EV2( " \( \displaystyle \sum_{n=0}^\infty \frac{(-1)^n 2^{2n} x^{2n}}{(2n)!} \) | ||
| 34 : | " ); | ||
| 35 : | |||
| 36 : | $ansStr3 =EV2( " \( \cos(2x) \) " ); | ||
| 37 : | |||
| 38 : | $questStr4 = EV2( " \( \displaystyle \sum_{n=0}^\infty \frac{(-1)^n 2x^{2n+1}}{2n+1} \) | ||
| 39 : | " ); | ||
| 40 : | |||
| 41 : | $ansStr4 =EV2( " \( 2 \arctan(x) \) " ); | ||
| 42 : | |||
| 43 : | @questions =( $questStr1,$questStr2,$questStr3,$questStr4); | ||
| 44 : | @answers =( $ansStr1,$ansStr2,$ansStr3,$ansStr4); | ||
| 45 : | |||
| 46 : | # Now randomize the questions: | ||
| 47 : | @slice = &NchooseK(4,4); | ||
| 48 : | @shuffle = &shuffle(scalar(@slice)); | ||
| 49 : | |||
| 50 : | TEXT(EV2(<<EOT)); | ||
| 51 : | |||
| 52 : | Match each of the Maclaurin series with right function. $BR | ||
| 53 : | |||
| 54 : | EOT | ||
| 55 : | TEXT( | ||
| 56 : | &match_questions_list(@questions[@slice]), | ||
| 57 : | &OL(@answers[@slice[@shuffle]]) | ||
| 58 : | ); | ||
| 59 : | ANS(str_cmp([@ALPHABET[&invert(@shuffle)]], filters=>["remove_whitespace","ignore_case"])); | ||
| 60 : | ##the correct answers are obtained by applying | ||
| 61 : | ##the inverse (adjoint) permutation to the captions. | ||
| 62 : | |||
| 63 : | ENDDOCUMENT(); # This should be the last executable line in the problem. | ||
| 64 : |
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