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# View of /trunk/NationalProblemLibrary/ma122DB/set3/s2_9_39.pg

Wed Jul 18 00:35:17 2007 UTC (5 years, 11 months ago) by jjholt
File size: 1092 byte(s)
Changed Stew4e to Stew 6e.


    1 ##KEYWORDS('derivatives', 'limits')
2 ##DESCRIPTION
3 ##  Evaluate some limits
4 ##ENDDESCRIPTION
5
6 ## Shotwell cleaned
7 ## tcao , PAID on 11-24-2003
8
9 ## DBsubject('Calculus')
10 ## DBchapter('Limits and Derivatives')
11 ## DBsection('The Derivative as a Function')
12 ## Date('6/3/2002')
13 ## Author('')
14 ## Institution('')
15 ## TitleText1('Calculus: Early Transcendentals')
16 ## EditionText1('6')
17 ## AuthorText1('Stewart')
18 ## Section1('2.8')
19 ## Problem1('39')
20
21 DOCUMENT();        # This should be the first executable line in the problem.
22
24 "PGbasicmacros.pl",
26 "PGauxiliaryFunctions.pl"
27 );
28
29 TEXT(beginproblem());
30 $showPartialCorrectAnswers = 1; 31 32$a1 = random(2,10,1);
33
34 BEGIN_TEXT
35 Let $$f(x) = |x-a1|$$. Evaluate the following limits.
36 $BR$BR
37 $$\lim_{x\to a1^-} \frac{f(x)-f(a1)}{x-a1}=$$ \{ans_rule(10) \}
38 $BR$BR
39 $$\lim_{x\to a1^+} \frac{f(x)-f(a1)}{x-a1}=$$ \{ans_rule(10) \}
40 $BR$BR
41 Thus the function $$f(x)$$ is not differentiable at \$a1.
42 END_TEXT
43
44 ANS(num_cmp(-1));
45 ANS(num_cmp(1));
46
47
48
49 ENDDOCUMENT();        # This should be the last executable line in the problem.