##KEYWORDS('Calculus') ##Tagged by ynw2d ##DBsubject('Calculus') ## DBchapter('Limits and Derivatives') ##DBsection('Continuity') DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGgraphmacros.pl", "PGauxiliaryFunctions.pl" ); TEXT(beginproblem()); $showPartialCorrectAnswers = 1;$a=random(-3,3,1); $b=non_zero_random(-2,3,1);$c=random(-3,2,1); $m1=random(-1,1,0.5);$m2=($b -$a)/2; $m3=($c - $b - 1)/2;$m4=random(-1,1,0.5); @slice = NchooseK(3,3); @colors = ("blue", "red", "green"); @sc = @colors[@slice]; #scrambled colors @sa = ('A','B','C')[@slice]; $f1 = FEQ("${m1}*(x+1)+$a for x in [-2,-1) using color:$sc[0] and weight:2"); $f2 = FEQ("${m2}*(x-1)+$b for x in (-1,1) using color=$sc[0] and weight:2"); $f3 = FEQ("${m3}*(x-3)+$c for x in [1,3) using color=$sc[0] and weight=2"); $f4 = FEQ("1+$a for x in [-1,-1] using color=$sc[0] and weight=2");$f5 = FEQ("${m4}*(x-3)+$c for x in (3,4] using color=$sc[0] and weight=2");$graph = init_graph(-3,-6,5,6,'axes'=>[0,0],'grid'=>[8,12]); ($f1Ref,$f2Ref,$f3Ref,$f4Ref,$f5Ref) = plot_functions($graph,$f1,$f2,$f3,$f4,$f5); TEXT(EV2(<200, width=>200)); TEXT(EV2(<$PAR b) $$\displaystyle \lim_{x \to -1^+} F(x)$$ = \ $PAR c) $$\displaystyle \lim_{x \to -1} F(x)$$ = \$PAR d) $$F(-1)$$ = \ $PAR e) $$\displaystyle \lim_{x \to 1^-} F(x)$$ = \$PAR f) $$\displaystyle \lim_{x \to 1^+} F(x)$$ = \ $PAR g) $$\displaystyle \lim_{x \to 1} F(x)$$ = \$PAR h) $$\displaystyle \lim_{x \to 3} F(x)$$ = \ $PAR i) $$F(3)$$ = \$PAR EOT $ap1 = 1 +$a; $bp1 = 1 +$b; ANS(num_cmp($a, strings=>['DNE'])) ; ANS(num_cmp($a, strings=>['DNE'])) ; ANS(num_cmp($a, strings=>['DNE'])) ; ANS(num_cmp($ap1, strings=>['DNE'])); ANS(num_cmp($b, strings=>['DNE'])) ; ANS(num_cmp($bp1, strings=>['DNE'])); ANS(num_cmp('DNE', strings=>['DNE'])) ; ANS(num_cmp(\$c, strings=>['DNE'])) ; ANS(num_cmp('DNE', strings=>['DNE'])) ; ENDDOCUMENT(); # This should be the last executable line in the problem.