View of /trunk/NationalProblemLibrary/Rochester/setDerivatives21LHospital/osu_dr_21_21.pg

    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 
    7 ## Tagged by sawblade
    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 
   23 loadMacros(
   24 "PG.pl",
   25 "PGbasicmacros.pl",
   26 "PGchoicemacros.pl",
   27 "PGanswermacros.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();