##DESCRIPTION ##KEYWORDS('integrals', 'improper') ## sbrummel tagged and PAID on 2-20-2004 ## DBsubject('Calculus') ## DBchapter('Techniques of Integration') ## DBsection('Improper Integrals') ## Date('6/3/2002') ## Author('Arnie Pizer') ## Institution('rochester') ## TitleText1('Calculus Early Transcendentals') ## EditionText1('4') ## AuthorText1('Stewart') ## Section1('7.8') ## Problem1('13,14') ##ENDDESCRIPTION DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl" ); TEXT(beginproblem()); $showPartialCorrectAnswers = 1;$a = random(2,9,1); $b = -1+($a); $test = (-1+((-1)**$a))/2; if ($test==-1) {$soln = 'INF'; } else { $soln =$test; } TEXT(EV2(<['INF', 'MINF', 'DIV'])); ENDDOCUMENT(); # This should be the last executable line in the problem. ________________________________________________________________________________ ##DESCRIPTION ##KEYWORDS('integrals', 'improper') ## sbrummel tagged and PAID on 2-20-2004 ## DBsubject('Calculus') ## DBchapter('Techniques of Integration') ## DBsection('Improper Integrals') ## Date('6/3/2002') ## Author('Arnie Pizer') ## Institution('rochester') ## TitleText1('Calculus Early Transcendentals') ## EditionText1('4') ## AuthorText1('Stewart') ## Section1('7.8') ## Problem1('24') ##ENDDESCRIPTION ## Before doing anything, we must import the macro definitions on the next few lines. DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl" ); TEXT(beginproblem()); $showPartialCorrectAnswers = 1;$a = random(1,6,1); $soln = arctan($a) + arcsin(1); TEXT(EV2(<8) { $questStr7 = EV2("$$\displaystyle \int_{1}^{\infty}s e^{-bb s^2}\,ds$$");$ansStr7 = "C"; } else { $questStr7 = EV2("$$\displaystyle \int_{1}^{\infty}s e^{bb s^2}\,ds$$");$ansStr7 = "D"; } $questStr8 = EV2("$$\displaystyle \int_{aa}^{a2}\ln(x-aa)\,dx$$");$ansStr8 = "C"; @questions =( $questStr1,$questStr2,$questStr3,$questStr4,$questStr5,$questStr6, $questStr7,$questStr8); @answers =( $ansStr1,$ansStr2,$ansStr3,$ansStr4,$ansStr5,$ansStr6, $ansStr7,$ansStr8); @shuffle = &shuffle(scalar(@questions)); TEXT( &match_questions_list(@questions[@shuffle]) ); ##set $PG_environment{'textbook'} in webworkCourse.ph if (defined($textbook)) { if ($textbook eq "EllisGulick5") { BEGIN_TEXT$PAR This problem covers section 7.7 of the text. For further practice, you should do 5-10 odd numbered problems from among problems 1-59 on pages 486-487. END_TEXT } } ANS(str_cmp([@answers[@shuffle] ])); ENDDOCUMENT(); ________________________________________________________________________________ ##KEYWORDS('integrals', 'improper') ##DESCRIPTION ## Determine if an improper integral exists and evaluate it. ##ENDDESCRIPTION ## Shotwell cleaned ## DBsubject('Calculus') ## DBchapter('Techniques of Integration') ## DBsection('Improper Integrals') ## Date('6/3/2002') ## Author('') ## Institution('') ## TitleText1('Calculus Early Transcendentals') ## EditionText1('4') ## AuthorText1('Stewart') ## Section1('7.8') ## Problem1('30') DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PGbasicmacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl" ); TEXT(beginproblem()); $showPartialCorrectAnswers = 1;$a = random(8,13,1); $b = random(1, 7);$soln = "3/2*$a*($a-$b)^(2/3)"; BEGIN_TEXT Determine whether the integral is divergent or convergent. If it is convergent, evaluate it.$BR$BR If it diverges to infinity, state your answer as$BITALIC inf $EITALIC . If it diverges to negative infinity, state your answer as$BITALIC -inf $EITALIC . If it diverges without being infinity or negative infinity, state your answer as$BITALIC div $EITALIC .$BR $\int_{b}^{a} \frac{a}{\sqrt[3]{x-b}} dx$ $BR Answer: \{ans_rule( 30) \}$BR END_TEXT ANS(num_cmp($soln, strings=>['inf', '-inf', 'div'])); ENDDOCUMENT(); ________________________________________________________________________________ ##KEYWORDS('integrals', 'improper') ##DESCRIPTION ## Determine if an improper integral converges and evaluate it. ##ENDDESCRIPTION ## Shotwell cleaned ## DBsubject('Calculus') ## DBchapter('Techniques of Integration') ## DBsection('Improper Integrals') ## Date('6/3/2002') ## Author('') ## Institution('') ## TitleText1('Calculus Early Transcendentals') ## EditionText1('4') ## AuthorText1('Stewart') ## Section1('7.8') ## Problem1('33') DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PGbasicmacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl" ); TEXT(beginproblem());$showPartialCorrectAnswers = 1; $a = -random(1,20,1);$b = random(1,20,1); $c = random(2,8,2); BEGIN_TEXT Determine whether the integral is divergent or convergent. If it is convergent, evaluate it.$BR$BR If it diverges to infinity, state your answer as$BITALIC inf $EITALIC . If it diverges to negative infinity, state your answer as$BITALIC -inf $EITALIC . If it diverges without being infinity or negative infinity, state your answer as$BITALIC div $EITALIC .$BR $\int_{a}^{b} \frac{1}{x^{c}} \, dx$ $BR Answer: \{ans_rule(40) \}$BR END_TEXT ANS(num_cmp('inf', strings=>['inf', '-inf', 'div'])); ENDDOCUMENT(); # This should be the last executable line in the problem. ________________________________________________________________________________ ##DESCRIPTION ##KEYWORDS('integrals', 'improper') ## sbrummel tagged and PAID on 2-20-2004 ## DBsubject('Calculus') ## DBchapter('Techniques of Integration') ## DBsection('Improper Integrals') ## Date('6/3/2002') ## Author('Arnie Pizer') ## Institution('rochester') ## TitleText1('Calculus Early Transcendentals') ## EditionText1('4') ## AuthorText1('Stewart') ## Section1('7.8') ## Problem1('20') ##ENDDESCRIPTION DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl" ); TEXT(beginproblem()); $showPartialCorrectAnswers = 1;$l = random(.1,.9,.1); $m = random(-1,1,2);$n = 1+($l*$m); $a=random(2,8,1);$b=random(2,5,1); $soln = (1+$a*$b)*exp(-$a*$b)/$b**2; TEXT(EV2(<['INF', 'MINF', 'DIV'])); ENDDOCUMENT(); # This should be the last executable line in the problem.