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Tue Nov 8 15:17:41 2011 UTC (2 years, 3 months ago) by aubreyja
File size: 1451 byte(s)
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('49')
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 $a = Real(random(2, 5, 1)); 22$b = Real(random(2, 5, 1));
23 $c = Real(random(1, 10, 1)); 24 25$t0 = Real(random(1, 10, 1));
26
27 $xt = Formula("t **$a");
28 $yt = Formula("t **$b - $c"); 29 30$anst = Formula("( ($b * t**($b - 1)) / ($a * t**($a - 1) ))")->reduce();
31
32 $fp =$anst->eval(t=>$t0); 33 34 35 Context()->texStrings; 36 BEGIN_TEXT 37 \{ beginproblem() \} 38 \{ textbook_ref_exact("Rogawski ET 2e", "11.1","49") \} 39$PAR
40 Find $$\frac{dy}{dx}$$ at the point t = $t0. 41$PAR
42 $$c(t) = (xt, yt)$$
43 $PAR 44 $$\frac{dy}{dx}$$ (at t =$t0) = \{ans_rule()\}
45 END_TEXT
46 Context()->normalStrings;
47
48 ANS($fp->cmp); 49 50 Context()->texStrings; 51 SOLUTION(EV3(<<'END_SOLUTION')); 52$PAR
53 $SOL 54 $$\frac{dy}{dx} = \frac{y'(t)}{x'(t)} = \frac{({yt})'}{({xt})'} = anst$$ 55$PAR
56 Substituting t = $t0 we get 57$PAR
58 $$\frac{dy}{dx} = fp$$.
59 END_SOLUTION
60
61 ENDDOCUMENT();
62