View of /trunk/NationalProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/10_Infinite_Series/10.7_Taylor_Series/10.7.1.pg

    1 # DBsubject('Calculus')
    2 # DBchapter('')
    3 # DBsection('')
    4 # KEYWORDS('')
    5 # TitleText1('Calculus: Early Transcendentals')
    6 # EditionText1('2')
    7 # AuthorText1('Rogawski')
    8 # Section1('10.7')
    9 # Problem1('1')
   10 # Author('Emily Price')
   11 # Institution('W.H.Freeman')
   12 DOCUMENT();
   13 
   14 
   15 
   16 #Load Necessary Macros
   17 
   18 loadMacros("PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", );
   19 loadMacros("Parser.pl");
   20 loadMacros("freemanMacros.pl");
   21 
   22 
   23 Context()->variables->add(n=>'Real');
   24 
   25 #Book Values
   26 #$base = 2;
   27 
   28 $constant1 = non_zero_random(-15, 15);
   29 $constant2 = non_zero_random(-15, 15);
   30 $constant3 = non_zero_random(-15, 15);
   31 $constant4 = non_zero_random(-15, 15);
   32 
   33 $maclaurin = Formula("$constant1 + $constant2*x + ($constant3*x^2)/2! + ($constant4*x^3)/3!")->reduce;
   34 
   35 Context()->texStrings;
   36 
   37 BEGIN_TEXT
   38 \{ beginproblem() \}
   39 \{ textbook_ref_exact("Rogawski ET 2e", "10.7", "1") \}
   40 $PAR
   41 Write out the first four terms of the Maclaurin series of \( f(x) \) if
   42 \[f(0) = $constant1, \qquad f'(0) = $constant2, \qquad f''(0) = $constant3, \qquad f'''(0) = $constant4 \]
   43 $PAR
   44 \( f(x) \) = \{ans_rule() \} \( + \cdots \)
   45 END_TEXT
   46 
   47 Context()->normalStrings;
   48 
   49 #Answer Check Time!
   50 ANS($maclaurin->cmp);
   51 
   52 Context()->texStrings;
   53 SOLUTION(EV3(<<'END_SOLUTION'));
   54 $PAR
   55 $SOL
   56 
   57 The first four terms of the Maclaurin series of \( f(x) \) are
   58 \[ f(0) + f'(0)x + \frac{f''(0)}{2!}x^2 + \frac{f'''(0)}{3!}x^3\]
   59 \[= $maclaurin.\]
   60 
   61 END_SOLUTION
   62 
   63 ENDDOCUMENT()