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| 1 : | jj | 61 | ## DESCRIPTION |
| 2 : | ## Calculus | ||
| 3 : | ## ENDDESCRIPTION | ||
| 4 : | |||
| 5 : | ## KEYWORDS('calculus', 'derivative') | ||
| 6 : | ## Tagged by YL | ||
| 7 : | |||
| 8 : | ## DBsubject('Calculus') | ||
| 9 : | ## DBchapter('Single Variable') | ||
| 10 : | ## DBsection('Differentiation') | ||
| 11 : | ## Date('') | ||
| 12 : | ## Author('') | ||
| 13 : | ## Institution('ASU') | ||
| 14 : | ## TitleText1('Calculus') | ||
| 15 : | ## EditionText1('5e') | ||
| 16 : | ## AuthorText1('Stewart') | ||
| 17 : | ## Section1('') | ||
| 18 : | ## Problem1('') | ||
| 19 : | |||
| 20 : | DOCUMENT(); | ||
| 21 : | |||
| 22 : | loadMacros( | ||
| 23 : | "PG.pl", | ||
| 24 : | "PGbasicmacros.pl", | ||
| 25 : | "PGchoicemacros.pl", | ||
| 26 : | "PGanswermacros.pl", | ||
| 27 : | "PGauxiliaryFunctions.pl" | ||
| 28 : | ); | ||
| 29 : | |||
| 30 : | TEXT(&beginproblem); | ||
| 31 : | $showpartialcorrectanswers = 1; | ||
| 32 : | |||
| 33 : | $a = random(.3,.9, .1); | ||
| 34 : | $b = random(1,5,1); | ||
| 35 : | $c = random(7,12,1); | ||
| 36 : | |||
| 37 : | TEXT(EV2(<<EOT)); | ||
| 38 : | A coal-burning electrical generating plant emits sulfur dioxide | ||
| 39 : | into the surrounding air. The concentration \(C(x)\), in parts per | ||
| 40 : | million, is approximately given by the function | ||
| 41 : | \[ C(x) = \frac{$a}{x^2}, \] | ||
| 42 : | where \(x\) is the distance away from the plant in miles. | ||
| 43 : | $BR | ||
| 44 : | The instantaneous rate of change of the sulfur dioxide | ||
| 45 : | concentration: | ||
| 46 : | $BR | ||
| 47 : | (A) $b miles from the plant = \{ans_rule(30) \} | ||
| 48 : | $BR | ||
| 49 : | EOT | ||
| 50 : | |||
| 51 : | $ans = (-2)*$a*(($b)**(-3)); | ||
| 52 : | &ANS(std_num_cmp($ans)); | ||
| 53 : | |||
| 54 : | TEXT(EV2(<<EOT)); | ||
| 55 : | (B) $c miles from the plant = \{ans_rule(30) \} | ||
| 56 : | $BR | ||
| 57 : | EOT | ||
| 58 : | |||
| 59 : | $ans = -2*$a*($c**(-3)); | ||
| 60 : | &ANS(std_num_cmp($ans)); | ||
| 61 : | |||
| 62 : | |||
| 63 : | ENDDOCUMENT(); |
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