[npl] / trunk / NationalProblemLibrary / Michigan / Chap9Sec5 / Q15.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

# Annotation of /trunk/NationalProblemLibrary/Michigan/Chap9Sec5/Q15.pg

Revision 1184 - (view) (download)

 1 : glarose 964 # DESCRIPTION 2 : # Problem from Calculus, single variable, Hughes-Hallett et al., 4th ed. 3 : # WeBWorK problem written by Gavin LaRose, 4 : # ENDDESCRIPTION 5 : 6 : ## KEYWORDS('calculus', 'integral', 'series', 'power series', 'interval of convergence', 'radius of convergence') 7 : ## Tagged by glr 02/08/09 8 : 9 : ## DBsubject('Calculus') 10 : ## DBchapter('Infinite Sequences and Series') 11 : ## DBsection('Power Series') 12 : ## Date('') 13 : ## Author('Gavin LaRose') 14 : ## Institution('University of Michigan') 15 : ## TitleText1('Calculus') 16 : ## EditionText1('4') 17 : ## AuthorText1('Hughes-Hallett') 18 : ## Section1('9.5') 19 : ## Problem1('15') 20 : 21 : ## Textbook tags 22 : ## HHChapter('Sequences and Series') 23 : ## HHSection('Power Series and Interval of Convergence') 24 : 25 : 26 : 27 : DOCUMENT(); 28 : 29 : loadMacros( 30 : "PGstandard.pl", 31 : "MathObjects.pl", 32 : "PGchoicemacros.pl", 33 : # "parserNumberWithUnits.pl", 34 : # "parserFormulaWithUnits.pl", 35 : # "parserFormulaUpToConstant.pl", 36 : # "PGcourse.pl", 37 : ); 38 : 39 : Context("Numeric"); 40 : $showPartialCorrectAnswers = 1; 41 : 42 :$a = random(1,5,1); 43 : $ad = ($a == 1) ? "" : $a; 44 : 45 :$which = list_random(0,1,2); 46 : if ( $which == 0 ) { 47 :$ser = "$ad x + " . (4*$a) . " x^2 + " . (9*$a) . " x^3 + " . 48 : (16*$a) . " x^4 + " . (25*$a) . " x^5 + \cdots"; 49 :$r = Compute("1"); 50 : } elsif ( $which == 1 ) { 51 :$a = 2 if ( $a == 1 ); 52 :$ser = "$ad x + " . ($a*$a) . " x^2 + " . ($a**3) . " x^3 + " . 53 : ($a**4) . " x^4 + " . ($a**5) . " x^5 + \cdots"; 54 : $r = Compute("1/$a"); 55 : } elsif ( $which == 2 ) { 56 :$a-=2 if ( $a > 3 ); 57 :$ad = ($a == 1) ? "" :$a; 58 : $ser = "$ad x + " . (4*$a*$a) . " x^2 + " . (9*($a**3)) . " x^3 + " . 59 : (16*($a**4)) . " x^4 + " . (25*($a**5)) . " x^5 + \cdots"; 60 :$r = Compute("1/$a"); 61 : } 62 : 63 : TEXT(beginproblem()); 64 : Context()->texStrings; 65 : BEGIN_TEXT 66 : 67 : Use the ratio test to find the radius of convergence of the power 68 : series 69 : $ser$ 70 : 71 : $$R =$$ \{ ans_rule(15) \} 72 :$BR 73 : ${BITALIC}(If the radius is infinite, enter${BBOLD}Inf$EBOLD for R.)$EITALIC 74 : 75 : END_TEXT 76 : Context()->normalStrings; 77 : 78 : ANS( $r->cmp() ); 79 : 80 : if ($which == 0 ) { 81 : $soln =<texStrings; 127 : SOLUTION(EV3(<<'END_SOLUTION')); 128 :$PAR SOLUTION $PAR 129 : 130 :$soln 131 : 132 : END_SOLUTION 133 : Context()->normalStrings; 134 : 135 : ENDDOCUMENT();

 aubreyja at gmail dot com ViewVC Help Powered by ViewVC 1.0.9