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Tue Nov 8 15:17:41 2011 UTC (2 years, 5 months ago) by aubreyja
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Rogawski problems contributed by publisher WHFreeman. These are a subset of the problems available to instructors who use the Rogawski textbook. The remainder can be obtained from the publisher.

    1 ## DBsubject('Calculus')
2 ## DBchapter('Introduction to Differential Equations')
3 ## DBsection('Parametric Equations')
4 ## KEYWORDS('calculus', 'parametric', 'parametric equations')
5 ## TitleText1('Calculus: Early Transcendentals')
6 ## EditionText1('2')
7 ## AuthorText1('Rogawski')
8 ## Section1('11.1')
9 ## Problem1('1')
10 ## Author('Christopher Sira')
11 ## Institution('W.H.Freeman')
12
13 DOCUMENT();
17
18 $context = Context("Point"); 19$context->variables->add(t=>'Real');
20
21 $a = Real(random(-10, 10, 1)); 22$b = Real(random(-10, 10, 1));
23 $c = Real(random(1, 5, 1)); 24$d = Real(random(-10, 10, 1));
25 $e = Real(random(-10, 10, 1)); 26$f = Real(random(1, 5, 1));
27
28
29 $xform = Formula("$a + $b * t **$c")->reduce();
30 $yform = Formula("$d + $e * t **$f")->reduce();
31
32 $t1 = 0; 33$t2 = $t1 + Real(random(1, 5, 1)); 34$t3 = $t2 + Real(random(1, 5, 1)); 35 36$ans1 = Point( $xform->eval(t=>$t1), $yform->eval(t=>$t1) );
37 $ans2 = Point($xform->eval(t=>$t2),$yform->eval(t=>$t2) ); 38$ans3 = Point( $xform->eval(t=>$t3), $yform->eval(t=>$t3) );
39
40
41
42 Context()->texStrings;
43 BEGIN_TEXT
44 \{ beginproblem() \}
45 \{ textbook_ref_exact("Rogawski ET 2e", "11.1","1") \}
46 $PAR 47 Find the coordinates at times t =$t1, $t2,$t3 of a particle following the path $$x = xform$$, $$y = yform$$.
48 $PAR 49 t =$t1: \{ans_rule()\}
50 $PAR 51 t =$t2: \{ans_rule()\}
52 $PAR 53 t =$t3: \{ans_rule()\}
54 END_TEXT
55 Context()->normalStrings;
56
57 ANS($ans1->cmp,$ans2->cmp, $ans3->cmp); 58 59 Context()->texStrings; 60 SOLUTION(EV3(<<'END_SOLUTION')); 61$PAR
62 $SOL 63 Substituting t =$t1, t = $t2, and t =$t3 into $$x = xform$$, $$y = yform$$ gives the coordinates of the particle at these times respectively.  that is,
64 $PAR 65 (t =$t1): $$x = \{xform->eval(t=>t1) \},\, y = \{yform->eval(t=>t1) \} \, \to \, ans1$$
66 $PAR 67 (t =$t2): $$x = \{xform->eval(t=>t2) \},\, y = \{yform->eval(t=>t2) \} \, \to \, ans2$$
68 $PAR 69 (t =$t3): $$x = \{xform->eval(t=>t3) \},\,y = \{yform->eval(t=>t3) \} \, \to \, ans3$$
70 \$PAR
71
72 END_SOLUTION
73
74 ENDDOCUMENT();
75