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# Annotation of /trunk/NationalProblemLibrary/ma122DB/set11/s5_3_3.pg

 1 : gage 5 ##DESCRIPTION 2 : ## Integrals - Fundamental theorem of calculus 3 : ##ENDDESCRIPTION 4 : ##KEYWORDS('integrals', 'fundamental theorem of calculus') 5 : 6 : ## Shotwell cleaned 7 : ## lcao , PAID on 11-24-2003 8 : 9 : ## DBsubject('Calculus') 10 : ## DBchapter('Integrals') 11 : ## DBsection('The Fundamental Theorem of Calculus') 12 : ## Date('6/3/2002') 13 : ## Author('') 14 : ## Institution('') 15 : jjholt 453 ## TitleText1('Calculus: Early Transcendentals') 16 : jjholt 479 ## EditionText1('6') 17 : gage 5 ## AuthorText1('Stewart') 18 : ## Section1('5.3') 19 : ## Problem1('3') 20 : 21 : DOCUMENT(); # This should be the first executable line in the problem. 22 : 23 : loadMacros("PGbasicmacros.pl", 24 : "PGanswermacros.pl", 25 : "PGauxiliaryFunctions.pl"); 26 : 27 : TEXT(beginproblem()); 28 : $showPartialCorrectAnswers = 1; 29 : 30 :$x1=random(2,6,1); 31 : $a1 = random(-1,1,2); 32 :$x2= $a1*$x1; 33 : $b1 = random(3,8,1); 34 :$c1 = random(-1,5,1); 35 : 36 : BEGIN_TEXT 37 : Let $$\displaystyle f(x) = \int_{c1}^x t^b1 dt$$. Evaluate the following. 38 : $BR 39 :$BR 40 : $$f'(x) =$$ $SPACE \{ans_rule(20)\}$BR 41 : $$f'(x2) =$$ \{ans_rule(20)\} 42 : END_TEXT 43 : 44 : $ans1="x^$b1"; 45 : $ans2="$x2^$b1"; 46 : 47 : ANS(fun_cmp($ans1)); 48 : ANS(num_cmp(\$ans2)); 49 : 50 : ENDDOCUMENT(); # This should be the last executable line in the problem.