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# View of /trunk/NationalProblemLibrary/270/setLimitsRates5Continuity/ur_lr_5_1.pg

Sat Sep 8 05:17:01 2007 UTC (5 years, 8 months ago) by sh002i
File size: 1516 byte(s)
Added tags for Rogawski's "Calculus: Early Transcendentals".


    1 ## DESCRIPTION
2 ##   Removable Discontinuity
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('Discontinuity', 'Removable')
6 ## Tagged by nhamblet
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Limits and Derivatives')
10 ## DBsection('Continuity')
11 ## Date('')
12 ## Author('')
13 ## Institution('ASU')
14 ## TitleText1('')
15 ## EditionText1('')
16 ## AuthorText1('')
17 ## Section1('')
18 ## Problem1('')
19 ## TitleText2('Calculus: Early Transcendentals')
20 ## EditionText2('1')
21 ## AuthorText2('Rogawski')
22 ## Section2('2.4')
23 ## Problem2('23')
24
25 DOCUMENT();        # This should be the first executable line in the problem.
26
28 "PG.pl",
29 "PGbasicmacros.pl",
30 "PGchoicemacros.pl",
32 "PGauxiliaryFunctions.pl"
33 );
34
35 TEXT(beginproblem());
36 $showPartialCorrectAnswers = 1; 37 38$a = random(1,5,1);
39 $b = random(2*$a+2,2*$a+6,1); 40$b2 = $b-2*$a;
41 $ab =$a*$b; 42 43 TEXT(EV2(<<EOT)); 44$BR
45 A function $$f(x)$$ is said to have a $BBOLD removable$EBOLD discontinuity at $$x=a$$ if:
46 $BR 47$BBOLD 1.$EBOLD $$f$$ is either not defined or not continuous at $$x=a$$.$BR
48 $BBOLD 2.$EBOLD $$f(a)$$ could either be defined or redefined so that the new function IS continuous at $$x=a$$.
49 $HR 50 Let $$f(x) =\frac{2x^2+b2 x -ab}{x-a}$$ 51$BR
52 Show that $$f(x)$$ has a removable discontinuity at $$x=a$$ and determine what value for $$f(a)$$ would make $$f(x)$$ continuous at $$x=a$$.
53 $BR 54 Must define $$f(a)=$$\{ans_rule(15)\}. 55$BR
56 EOT
57
58 $ans = 2*$a+$b; 59 ANS(num_cmp($ans));
60
61 ENDDOCUMENT();        # This should be the last executable line in the problem.
62