View of /trunk/NationalProblemLibrary/ma123DB/set8/s10_2_9.pg

    1 ##KEYWORDS('parametric equation', 'tangent line')
    2 ##DESCRIPTION
    3 ## Find tangent line of a parametrized curve
    4 ##ENDDESCRIPTION
    5 
    6 ## Shotwell cleaned
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Parametric Equations and Polar Coordinates')
   10 ## DBsection('Tangents and Areas')
   11 ## Date('6/3/2002')
   12 ## Author('')
   13 ## Institution('')
   14 ## TitleText1('Calculus: Early Transcendentals')
   15 ## EditionText1('4')
   16 ## AuthorText1('Stewart')
   17 ## Section1('10.2')
   18 ## Problem1('9')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23 "PGbasicmacros.pl",
   24 "PGanswermacros.pl",
   25 );
   26 
   27 TEXT(beginproblem());
   28 $showPartialCorrectAnswers = 1;
   29 
   30 $a = random(1,9);
   31 $a2 = $a**2;
   32 
   33 BEGIN_TEXT
   34 If \( x = e^t \) and \( y = (t-$a)^2 \), find
   35 an equation \(y=mx+b\) of the tangent to the curve at \( (1,$a2) \).
   36 $BR$BR
   37 \(m=\) \{ans_rule( 20) \}
   38 $BR
   39 \(b=\) \{ans_rule( 20) \}
   40 END_TEXT
   41 
   42 ANS(num_cmp(-2*$a));
   43 ANS(num_cmp("2*$a+$a2"));
   44 
   45 ENDDOCUMENT();        # This should be the last executable line in the problem.