View of /trunk/NationalProblemLibrary/ASU-topics/setProductQuotientRule/3-5-35.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Differentiation' 'Product Rule' 'Quotient Rule')
    6 ## Tagged by tda2d
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Differentiation')
   10 ## DBsection('The Product and Quotient Rules')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('ASU')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 
   21 DOCUMENT();
   22 
   23 loadMacros(
   24 "PG.pl",
   25 "PGbasicmacros.pl",
   26 "PGchoicemacros.pl",
   27 "PGanswermacros.pl",
   28 "PGauxiliaryFunctions.pl"
   29 );
   30 
   31 TEXT(beginproblem());
   32 $showpartialcorrectanswers = 1;
   33 
   34 $a = random(2, 13, 1);
   35 $b = random(2,7,1);
   36 $c = random(2,7,1);
   37 $x0 = random(1,12,1);
   38 $y0 = ($x0 - $a)/($b*$x0 + $c);
   39 $m = (($b*$x0 + $c) - $b*($x0 - $a))/($b*$x0 + $c)**2;
   40 
   41 TEXT(EV2(<<EOT));
   42 Let
   43 \[ f(x) = \frac{x - $a}{$b x + $c}. \]
   44 Find an equation for the tangent line to the graph of \(f\)
   45 at \(x = $x0\).
   46 $BR
   47 Tangent line: \( y \) = \{ans_rule(40) \}
   48 $BR
   49 $BR
   50 EOT
   51 
   52 ANS(fun_cmp("$m*(x-$x0) + $y0", vars=>"x"));
   53 
   54 ENDDOCUMENT();