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# View of /trunk/NationalProblemLibrary/Rochester/setIntegrals0Theory/osu_in_0_16.pg

Sat Sep 8 05:17:01 2007 UTC (5 years, 8 months ago) by sh002i
File size: 1807 byte(s)
Added tags for Rogawski's "Calculus: Early Transcendentals".


    1 ## DESCRIPTION
2 ## Calculus
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('integral' 'summation' 'area' 'riemann')
6 ## Tagged by tda2d
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Integrals')
10 ## DBsection('Area and Distance')
11 ## Date('')
12 ## Author('')
13 ## Institution('Rochester')
14 ## TitleText1('')
15 ## EditionText1('')
16 ## AuthorText1('')
17 ## Section1('')
18 ## Problem1('')
19 ## TitleText2('Calculus: Early Transcendentals')
20 ## EditionText2('1')
21 ## AuthorText2('Rogawski')
22 ## Section2('5.2')
23 ## Problem2('29')
24
25 DOCUMENT();
26
28 "PG.pl",
29 "PGbasicmacros.pl",
30 "PGchoicemacros.pl",
32 "PGauxiliaryFunctions.pl"
33 );
34
35
36 $showPartialCorrectAnswers = 1; 37 38$a = random(2,7,1);
39 $b =$a + random(1,4,1);
40 $c = random(2,6,1); 41$c2 = 2*$c; 42$c3 = 3*$c; 43$answ = 2*($b+$c)**1.5/3 - 2*$b**1.5/3; 44 45 TEXT(beginproblem()); 46 BEGIN_TEXT 47 The following sum 48 $49 \sqrt{b + \frac{c}{n}} \cdot \left( \frac{c}{n}\right) + 50 \sqrt{b + \frac{c2}{n}} \cdot \left( \frac{c}{n}\right) + 51 \ldots + \sqrt{b + \frac{c n}{n}} \cdot \left( \frac{c}{n}\right) 52$ 53 54 is a right Riemann sum for the definite integral 55 $\int_{a}^b f(x)\, dx$ 56$BR
57
58 where $$b$$ = \{ ans_rule()\}
59 $BR 60 61 and $$f(x)$$ = \{ ans_rule()\} 62$PAR
63
64 It is also a Riemann sum for the definite integral
65 $\int_{b}^c g(x)\, dx$
66 $BR 67 68 where $$c$$ = \{ ans_rule()\} 69$BR
70
71 and $$g(x)$$ =  \{ ans_rule()\}
72 $PAR 73 74 The limit of these Riemann sums as $$n \to \infty$$ is 75 \{ ans_rule(40)\} 76 END_TEXT 77 78 ##set$PG_environment{'textbook'} in webworkCourse.ph
79 if (defined($textbook)) { 80 if ($textbook eq "EllisGulick5") {
81 BEGIN_TEXT
82 $PAR 83$BBOLD Hint:$EBOLD This is similar to Problem 7 in WeBWorK Problem Set Hmwk \#1. 84 END_TEXT 85 } 86 } 87 88 ANS(num_cmp($a + $c)); 89 ANS(fun_cmp("sqrt($b - $a + x)", vars=>"x")); 90 ANS(num_cmp($b + $c)); 91 ANS(fun_cmp("sqrt(x)", vars=>"x")); 92 ANS(num_cmp($answ));
93
94 ENDDOCUMENT();
95