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| 1 : | gage | 5 | ##DESCRIPTION |
| 2 : | ##Calculus: Differentiation | ||
| 3 : | ##ENDDESCRIPTION | ||
| 4 : | |||
| 5 : | ##KEYWORDS('calculus', 'differentiation') | ||
| 6 : | ##Tagged by YJ | ||
| 7 : | |||
| 8 : | ## DBsubject('Calculus') | ||
| 9 : | ## DBchapter('Differentiation') | ||
| 10 : | ## DBsection('The Product and Quotient Rules') | ||
| 11 : | ## Date('5/26/2005') | ||
| 12 : | ## Author('Jeff Holt') | ||
| 13 : | ## Institution('UVA') | ||
| 14 : | jjholt | 480 | ## TitleText1('Calculus: Early Transcendentals') |
| 15 : | ## EditionText1('5') | ||
| 16 : | gage | 5 | ## AuthorText1('Stewart') |
| 17 : | ## Section1('3.2') | ||
| 18 : | ## Problem1('23') | ||
| 19 : | |||
| 20 : | jjholt | 481 | ## TitleText2('Calculus: Early Transcendentals') |
| 21 : | ## EditionText2('6') | ||
| 22 : | ## AuthorText2('Stewart') | ||
| 23 : | ## Section2('3.2') | ||
| 24 : | ## Problem2('') | ||
| 25 : | |||
| 26 : | gage | 5 | DOCUMENT(); # This should be the first executable line in the problem. |
| 27 : | |||
| 28 : | loadMacros("PG.pl", | ||
| 29 : | "PGbasicmacros.pl", | ||
| 30 : | "PGchoicemacros.pl", | ||
| 31 : | "PGanswermacros.pl", | ||
| 32 : | "PGauxiliaryFunctions.pl"); | ||
| 33 : | |||
| 34 : | $a = random(2,8,1); | ||
| 35 : | $b = random(2,8,1); | ||
| 36 : | |||
| 37 : | $x0 = random(1,3,1); | ||
| 38 : | $y0 = ($a*$x0)/($b+$x0); | ||
| 39 : | $m = ($a*$b)/($x0 + $b)**2; | ||
| 40 : | |||
| 41 : | TEXT(beginproblem()); | ||
| 42 : | |||
| 43 : | $showPartialCorrectAnswers = 1; | ||
| 44 : | |||
| 45 : | |||
| 46 : | TEXT(EV2(<<EOT)); | ||
| 47 : | Find an equation for the line tangent to the graph of | ||
| 48 : | \[ | ||
| 49 : | f(x) = \frac{$a x}{x + $b} | ||
| 50 : | \] | ||
| 51 : | at the point ($x0, $y0). | ||
| 52 : | $PAR | ||
| 53 : | $PAR | ||
| 54 : | \(y\) = \{ans_rule(30)\} | ||
| 55 : | |||
| 56 : | EOT | ||
| 57 : | |||
| 58 : | $ans = "$y0 + $m*(x-$x0)"; | ||
| 59 : | |||
| 60 : | ANS(fun_cmp($ans, vars=>"x")); | ||
| 61 : | |||
| 62 : | ENDDOCUMENT(); # This should be the last executable line in the problem. |
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