[npl] / trunk / NationalProblemLibrary / WHFreeman / Rogawski_Calculus_Early_Transcendentals_Second_Edition / 14_Differentiation_in_Several_Variables / 14.7_Optimization_in_Several_Variables / 14.7.28.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

# Annotation of /trunk/NationalProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/14_Differentiation_in_Several_Variables/14.7_Optimization_in_Several_Variables/14.7.28.pg

 1 : aubreyja 2584 ## DBsubject('Calculus') 2 : ## DBchapter('Differentiation in Several Variables') 3 : ## DBsection('Optimization in Several Variables') 4 : ## KEYWORDS('calculus') 5 : ## TitleText1('Calculus: Early Transcendentals') 6 : ## EditionText1('2') 7 : ## AuthorText1('Rogawski') 8 : ## Section1('14.7') 9 : ## Problem1('28') 10 : ## Author('JustAsk - Vladimir Finkelshtein') 11 : ## Institution('W.H.Freeman') 12 : 13 : DOCUMENT(); 14 : 15 : loadMacros("PG.pl","PGbasicmacros.pl","PGanswermacros.pl"); 16 : loadMacros("Parser.pl"); 17 : loadMacros("freemanMacros.pl"); 18 : loadMacros("PGauxiliaryFunctions.pl"); 19 : loadMacros("PGgraphmacros.pl"); 20 : loadMacros("PGchoicemacros.pl"); 21 : 22 : TEXT(beginproblem()); 23 : 24 : Context()->texStrings; 25 : $context = Context(); 26 :$context->variables->add(y=>'Real'); 27 : $r=random(1,5,1); 28 :$a=random(-5,5,1); 29 : $b=$a+random(1,5,1); 30 : $c=random(-5,5,1); 31 :$d=$d+random(1,5,1); 32 : 33 :$r1=$r+1; 34 :$q=random(1,6,1); 35 : if($q==1) { 36 :$quest="$$x^2+y^2 \le r$$"; 37 : $ans1="closed"; 38 :$wrong1="not closed"; 39 : $ans2="bounded"; 40 :$wrong2="not bounded"; 41 : $sol="This domain is bounded since it is contained, for instance, in the disk $$x^2+y^2<r1$$. The domain is also closed since it contains all of its boundary points, which are the points of the circle $$x^2+y^2=r$$"; } 42 : 43 : if($q==2) { 44 : $quest="$$x^2+y^2 < r$$"; 45 :$ans1="not closed"; 46 : $wrong1="closed"; 47 :$ans2="bounded"; 48 : $wrong2="not bounded"; 49 :$sol="This domain is bounded since it is contained, for instance, in the disk $$x^2+y^2<r1$$. It is not closed since its boundary $$x^2+y^2=r$$is not contained in the domain"; } 50 : 51 : 52 : if($q==3) { 53 :$quest="$$x \ge r$$"; 54 : $ans1="closed"; 55 :$wrong1="not closed"; 56 : $ans2="not bounded"; 57 :$wrong2="bounded"; 58 : $sol="This domain is not contained in any disk, hence it is not bounded. However, the domain contains all its boundary $$x=r$$, hence it is closed."; } 59 : 60 : if($q==4) { 61 : $quest="$$x > 0, y > 0$$"; 62 :$ans1="not closed"; 63 : $wrong1="closed"; 64 :$ans2="not bounded"; 65 : $wrong2="bounded"; 66 :$sol="This domain is not contained in any disk, hence it is not bounded. The boundary is the positive $$x$$ and $$y$$ axes, and it is not contained in the domain, therefore the domain is not closed"; } 67 : 68 : if($q==5) { 69 :$quest="$$a \le x \le b, c \le y \le d$$"; 70 : $ans1="closed"; 71 :$wrong1="not closed"; 72 : $ans2="bounded"; 73 :$wrong2="not bounded"; 74 : $sol="This domain is contained in the disk $$x^2+y^2=10^2$$, hence it is bounded. Moreover, the domain contains its boundary, therefore the domain is closed"; } 75 : 76 : if($q==6) { 77 : $quest="$$x^2+y^2 \le r, x>0$$"; 78 :$ans1="not closed"; 79 : $wrong1="closed"; 80 :$ans2="bounded"; 81 : $wrong2="not bounded"; 82 :$sol="This domain is bounded since it is contained, for instance, in the disk $$x^2+y^2<r1$$. It is not closed since the part $$\lbrace (0,y) \in \Re^2:|y|\le \sqrt{r} \rbrace$$ of its boundary is not containe in the domain"; } 83 : 84 : $mc = new_multiple_choice(); 85 :$mc -> qa ("$$\lbrace (x,y)\in \Re^2:$$ $quest $$\rbrace$$","$ans1",); 86 : $mc ->extra("$wrong1",); 87 : $mc2 = new_multiple_choice(); 88 :$mc2 -> qa ("","$ans2",); 89 :$mc2 ->extra("$wrong2",); 90 : 91 : BEGIN_TEXT 92 : \{ textbook_ref_exact("Rogawski ET 2e", "14.7","28") \} 93 :$PAR 94 : Determine whether the domain 95 : \{$mc -> print_q\} is 96 : \{$mc -> print_a\} 97 : \{$mc2 -> print_a\}$PAR 98 : $BR 99 : END_TEXT 100 : 101 : Context()->normalStrings; 102 : ANS(str_cmp($mc->correct_ans)); 103 : ANS(str_cmp($mc2->correct_ans)); 104 : Context()->texStrings; 105 : 106 : SOLUTION(EV3(<<'END_SOLUTION')); 107 :$PAR 108 : $SOL 109 :$BR 110 : $sol 111 :$BR 112 : END_SOLUTION 113 : 114 : ENDDOCUMENT();