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Tue Nov 8 15:17:41 2011 UTC (2 years, 5 months ago) by aubreyja
File size: 1478 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('Parametric Equations, Polar Coordinates, and Conic Sections')
3 ## DBsection('Arc Length and Speed')
4 ## KEYWORDS('calculus', 'parametric', 'polar', 'conic')
5 ## TitleText1('Calculus: Early Transcendentals')
6 ## EditionText1('2')
7 ## AuthorText1('Rogawski')
8 ## Section1('11.2')
9 ## Problem1('1')
10 ## Author('Christopher Sira')
11 ## Institution('W.H.Freeman')
12
13 DOCUMENT();
19 $context = Context(); 20 21 22$a = random(2, 9);
23 $b = random(2, 9); 24$coeff = Formula("($a**2 + (-1 *$b)**2) ** .5");
25
26 #$ans = Formula("$coeff * 2");
27 $ans = Compute("2*sqrt($a**2 + $b**2)"); 28 29 30 Context()->texStrings; 31 BEGIN_TEXT 32 \{ beginproblem() \} 33 \{ textbook_ref_exact("Rogawski ET 2e", "11.2","1") \} 34$PAR
35 Use equation 4 to calculate the length of the path over the given interval.
36 $c(t) = (a t + 1, 9 - b t), \, 0 \le t \le 2$
37 $PAR 38 \{ ans_rule() \} 39$PAR
40 END_TEXT
41 Context()->normalStrings;
42
43 ANS($ans->cmp); 44 45 Context()->texStrings; 46 SOLUTION(EV3(<<'END_SOLUTION')); 47$PAR
48 \$SOL
49 Since $$x = a t + 1$$ and $$y = 9 - b t$$ we have $$x' = a$$ and $$y' = - b$$.  Hence, the length of the path is
50 $S = \int ^2 _0 \sqrt{a^2 + (- b)^2} \, dt = coeff \int ^2 _0 \, dt = 2\sqrt{\{a**2 + b**2\}} = ans$
51 END_SOLUTION
52
53 ENDDOCUMENT();