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Tue Apr 11 16:55:13 2006 UTC (7 years, 1 month ago) by jjholt
File size: 1902 byte(s)
Added tags.  --JH


    1 ## DESCRIPTION
2 ## Algebra: Exponential and Logarithmic Functions
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS ('exponential')
6 ## Tagged by cmd6a 4/4/06
7
8 ## DBsubject('Algebra')
9 ## DBchapter('Exponential and Logarithmic Functions')
10 ## DBsection('The Natural Exponential Function')
11 ## Date('')
12 ## Author('')
13 ## Institution('Rochester')
14 ## TitleText1('')
15 ## EditionText1('')
16 ## AuthorText1('')
17 ## Section1('')
18 ## Problem1('')
19
20 DOCUMENT();        # This should be the first executable line in the problem.
21
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.pl",
27 "PGauxiliaryFunctions.pl"
28 );
29
30 TEXT(beginproblem());
31 $showPartialCorrectAnswers = 1; 32 33$a = random(-10,10,1);
34 $b = non_zero_random(-10,10,1); 35$c = non_zero_random(-10,10,1);
36
37 $y = random(1,10,1); 38$x = 2*$y; 39 40$p = random(1,10,1);
41 $q = non_zero_random(-10,10,1); 42$r = random(1,10,1);
43 $s = non_zero_random(-10,10,1); 44 45 BEGIN_TEXT; 46 Simplify the following expressions. Give exact answers with the fewest number 47 of $$e$$'s possible. Then give a decimal approximation. 48$BR$BR 49 (a) $e^{a} e^{b} e^{c} =$ \{ans_rule(10)\}, which is approximately 50 \{ans_rule(10)\}. 51$BR$BR 52 (b) $\frac{e^{x} - e^{-x}}{e^{y} - e^{-y}} =$ \{ans_rule(10)\}, 53 which is approximately \{ans_rule(10)\}. 54$BR$BR 55 (c) $(e^{p} + q)(e^{r} + s) =$ \{ans_rule(10)\}, which is approximately 56 \{ans_rule(10)\} 57 58 END_TEXT; 59 60$exp1 = $a+$b+$c; 61$ans1 = "e**$exp1"; 62$ans2 = $E**$exp1;
63
64 ANS(fun_cmp($ans1,var=>['e'])); 65 ANS(num_cmp($ans2, mode=>"strict"));
66
67 $ans3 = "(e**$x+1)/(e**$y)"; 68$ans4 = ($E**$x+1)/($E**$y);
69
70 ANS(fun_cmp($ans3,var=>['e'])); 71 ANS(num_cmp($ans4, mode=>"strict"));
72
73 $ans5 = "e**($p+$r) +$s*e**$p +$q*e**$r +$q*$s"; 74$ans6 = $E**($p+$r) +$s*$E**$p + $q*$E**$r+$q*$s; 75 76 ANS(fun_cmp($ans5,var=>['e']));
77 ANS(num_cmp(\$ans6, mode=>"strict"));
78 ENDDOCUMENT();        # This should be the last executable line in the problem.
79


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