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Revision 2584 - (download) (annotate)
Tue Nov 8 15:17:41 2011 UTC (2 years, 5 months ago) by aubreyja
File size: 2011 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('21')
   10 ## Author('Christopher Sira')
   11 ## Institution('W.H.Freeman')
   12 
   13 DOCUMENT();
   14 loadMacros("PG.pl","PGbasicmacros.pl","PGanswermacros.pl");
   15 loadMacros("Parser.pl");
   16 loadMacros("freemanMacros.pl");
   17 
   18 $context = Context("Interval");
   19 $context->variables->add(t=>'Real');
   20 
   21 $temp = random(0, 1, 1);
   22 $a = "lower";
   23 $ans = Interval( "[pi, 2 * pi]");
   24 
   25 $explain = "For \( t = \pi \), we have \( c(\pi) = (-1, 0) \).  As t increases from \( \pi \) to \( 2\pi \), the x-coordinate of \( c(t) \) increases from -1 to 1, and the y-coordinate decreases from 0 to -1 (at \( t = \frac{3\pi}{2} \)) and then returns to 0.  Thus, for t in \( $ans \), the equation traces the $a part of the circle.";
   26 
   27 if ($temp == 0) {
   28     $a = "upper";
   29     $ans = Interval("[0, pi]");
   30     $explain = "For \( t = 0 \), we have \( c(\pi) = (1, 0) \).  As t increases from \( 0 \) to \( \pi \), the x-coordinate of \( c(t) \) decreases from 1 to -1, and the y-coordinate increases from 0 to 1 (at \( t = \frac{\pi}{2} \)) and then returns to 0.  Thus, for t in \( $ans \), the equation traces the $a part of the circle.";
   31 
   32 }
   33 
   34 
   35 
   36 Context()->texStrings;
   37 BEGIN_TEXT
   38 \{ beginproblem() \}
   39 \{ textbook_ref_exact("Rogawski ET 2e", "11.1","21") \}
   40 $PAR
   41 Find an interval of t-values such that \( c(t) = (\cos{t}, \sin{t}) \) traces the $a half of the unit circle (in the counter-clockwise direction).
   42 $PAR
   43 interval = \{ans_rule()\}
   44 $PAR
   45 Note: Use lowercase "pi" for \( \pi \).
   46 $PAR
   47 Example answer: \( \{Interval("[0, 1]") \}\).
   48 $PAR
   49 END_TEXT
   50 Context()->normalStrings;
   51 
   52 ANS($ans->cmp);
   53 
   54 Context()->texStrings;
   55 SOLUTION(EV3(<<'END_SOLUTION'));
   56 $PAR
   57 $SOL
   58 $explain
   59 END_SOLUTION
   60 
   61 ENDDOCUMENT();
   62 

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