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| 1 : | jj | 62 | ## DESCRIPTION |
| 2 : | ## Calculus | ||
| 3 : | ## ENDDESCRIPTION | ||
| 4 : | |||
| 5 : | ## KEYWORDS('calculus', 'integrals') | ||
| 6 : | ## Tagged by YL | ||
| 7 : | |||
| 8 : | ## DBsubject('Calculus') | ||
| 9 : | ## DBchapter('Integrals') | ||
| 10 : | ## DBsection('The Fundamental Theorem of Calculus') | ||
| 11 : | ## Date('') | ||
| 12 : | ## Author('') | ||
| 13 : | ## Institution('ASU') | ||
| 14 : | jjholt | 473 | ## TitleText1('Calculus: Early Transcendentals') |
| 15 : | ## EditionText1('5') | ||
| 16 : | jj | 62 | ## AuthorText1('Stewart') |
| 17 : | jjholt | 473 | ## Section1('5.3') |
| 18 : | jj | 62 | ## Problem1('') |
| 19 : | |||
| 20 : | jjholt | 481 | ## TitleText2('Calculus: Early Transcendentals') |
| 21 : | ## EditionText2('6') | ||
| 22 : | ## AuthorText2('Stewart') | ||
| 23 : | ## Section2('5.3') | ||
| 24 : | ## Problem2('') | ||
| 25 : | |||
| 26 : | jj | 62 | ## Before doing anything, we must import the macro definitions on the next few lines. |
| 27 : | |||
| 28 : | DOCUMENT(); # This should be the first executable line in the problem. | ||
| 29 : | |||
| 30 : | loadMacros( | ||
| 31 : | "PG.pl", | ||
| 32 : | "PGbasicmacros.pl", | ||
| 33 : | "PGchoicemacros.pl", | ||
| 34 : | "PGanswermacros.pl", | ||
| 35 : | "PGauxiliaryFunctions.pl" | ||
| 36 : | ); | ||
| 37 : | |||
| 38 : | gage | 268 | TEXT(beginproblem()); |
| 39 : | jj | 62 | $showPartialCorrectAnswers = 1; |
| 40 : | |||
| 41 : | $a=random(2, 3, 1); | ||
| 42 : | $aa=$a**2; | ||
| 43 : | $aaa=$a**3; | ||
| 44 : | $funct = " 2/$aaa - (($a^2*t^2 + 2*$a*t + 2)*e^(-$a*t))/$aaa"; | ||
| 45 : | |||
| 46 : | TEXT(EV2(<<EOT)); | ||
| 47 : | A particle that moves along a straight line has velocity | ||
| 48 : | \[ v(t) = t^2 e^{-$a t} \] | ||
| 49 : | meters per second after t seconds. Find the distance the particle | ||
| 50 : | travels during the | ||
| 51 : | first t seconds. | ||
| 52 : | $BR $BR \{ans_rule(45) \} meters | ||
| 53 : | $BR | ||
| 54 : | $BBOLD Note: $EBOLD Your answer should be a function of \( t\). | ||
| 55 : | EOT | ||
| 56 : | |||
| 57 : | $ans = $funct; | ||
| 58 : | gage | 268 | ANS(fun_cmp($ans, vars=>"t")); |
| 59 : | jj | 62 | |
| 60 : | ENDDOCUMENT(); # This should be the last executable line in the problem. |
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