##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(<<EOT));
Let F be the function below.$PAR
EOT

TEXT(image( insertGraph($graph) , height=>200, width=>200));

TEXT(EV2(<<EOT));
$BR
$BR
Evaluate each of the following expressions.  $PAR
Note:  Enter 'DNE' if the limit does not exist or is not defined. $PAR

a) \( \displaystyle \lim_{x \to -1^-} F(x) \) = \<ans_rule(4)\>
$PAR

b) \( \displaystyle \lim_{x \to -1^+} F(x) \) = \<ans_rule(4)\>
$PAR

c) \( \displaystyle \lim_{x \to -1} F(x) \) = \<ans_rule(4)\>
$PAR

d) \( F(-1) \) = \<ans_rule(4)\>
$PAR

e) \( \displaystyle \lim_{x \to 1^-} F(x) \) = \<ans_rule(4)\>
$PAR

f) \( \displaystyle \lim_{x \to 1^+} F(x) \) = \<ans_rule(4)\>
$PAR

g) \( \displaystyle \lim_{x \to 1} F(x) \) = \<ans_rule(4)\>
$PAR

h) \( \displaystyle \lim_{x \to 3} F(x) \) = \<ans_rule(4)\>
$PAR

i) \( F(3) \) = \<ans_rule(4)\>
$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.