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Fri Jun 9 20:01:08 2006 UTC (6 years, 11 months ago) by jjholt
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    1 ##DESCRIPTION
2 ##KEYWORDS('derivatives', 'L'Hopital's rule')
3 ##  Find limits using L'Hopital's rule
4 ##Authored by Zig Fiedorowicz 2/4/2000
5 ##ENDDESCRIPTION
6
8
9 ## DBsubject('Calculus')
10 ## DBchapter('Applications of Differentiation')
11 ## DBsection('Indeterminate Forms and L'Hospital's Rule')
12 ## Date('2/4/2000')
13 ## Author('')
14 ## Institution('Rochester')
15 ## TitleText1('')
16 ## EditionText1('')
17 ## AuthorText1('')
18 ## Section1('')
19 ## Problem1('')
20
21 DOCUMENT();
22
24 "PG.pl",
25 "PGbasicmacros.pl",
26 "PGchoicemacros.pl",
28 "PGauxiliaryFunctions.pl"
29 );
30 $showPartialCorrectAnswers = 1; 31 32$AA = random(3,6,1);
33 $BB = random(2,7,1); 34$CC = random(3,12,1);
35
36 TEXT(beginproblem());
37 BEGIN_TEXT
38 Find the following limits, using L'H\^opital's rule, if appropriate.
39 Use INF to denote $$\infty$$ and MINF to denote $$-\infty$$
40 $PAR 41 42 (a) $$\displaystyle \lim_{x\to\infty}\frac{\tan^{-1}(x/AA)}{\sin^{-1}(1/x)}$$ = \{ ans_rule()\} 43$PAR
44
45 (b) $$\displaystyle \lim_{x\to 0}\frac{x\cos^5(\pi e^{x^{CC}})}{\ln(1 + BB x)}$$  =  \{ ans_rule()\}
46
47
48 END_TEXT
49
50 ANS(num_cmp("INF", strings=>["INF","MINF"]));
51 ANS(num_cmp(-1/\$BB, strings=>["INF","MINF"]));
52
53 ENDDOCUMENT();