[npl] / trunk / NationalProblemLibrary / Rochester / setDerivatives0Theory / s2_R_1-16.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

View of /trunk/NationalProblemLibrary/Rochester/setDerivatives0Theory/s2_R_1-16.pg

Wed Jun 27 19:45:04 2007 UTC (5 years, 10 months ago) by jjholt
File size: 3662 byte(s)
Updated/Corrected tags.  --JJH


    1 ## DESCRIPTION
2 ## Calculus
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS ('limit')
6 ## Tagged by cmd6a 4/20/06
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Limits and Derivatives')
10 ## DBsection('The Limit of a 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 $showPartialCorrectAnswers = 0; 32 33 TEXT(EV2(<<EOT)); 34 Enter a T or an F in each answer space below 35 to indicate whether the corresponding statement is true or 36 false. A statement is true only if it is true for all possibilities. 37 You must get all of the answers correct to receive credit. 38$BR
39 EOT
40 $x1 = random(1,3,1); 41$a1 = random(2,7,1);
42 $b1 =$x1**2 + $a1*$x1;
43 $c1 = random(3,9,1); 44$d1 = $x1**2 +$c1*$x1; 45$questStr1 = EV2(" $$\displaystyle \lim_{x\rightarrow x1}\frac 46 {x^2+a1 x- b1}{x^2+c1 x- d1} = \frac 47 {\displaystyle \lim_{x\rightarrow x1} x^2+a1 x- b1}{\lim_{x\rightarrow x1} x^2+c1 x- d1}$$");
48 $ansStr1 = "F"; 49 50$e1 = $x1**2+$a1*$x1-1; 51$f1 = $x1**2+$c1*$x1-2; 52$questStr2 = EV2(" $$\displaystyle \lim_{x\rightarrow x1}\frac 53 {x^2+a1 x- e1}{x^2+c1 x- f1} = \frac 54 {\displaystyle \lim_{x\rightarrow x1} x^2+a1 x- e1}{\displaystyle \lim_{x\rightarrow x1} x^2+c1 55 x- f1}$$");
56 $ansStr2 = "T"; 57 58$x3 = random(1,7,1);
59 $questStr3 = EV2(" If $$\displaystyle \lim_{x\rightarrow x3} f(x) = a1$$ 60 and $$\displaystyle \lim_{x\rightarrow x3} g(x) = 0$$, then $$\displaystyle \lim_{x\rightarrow x3} 61 [f(x)/g(x)]$$ 62 does not exist"); 63$ansStr3 = "T";
64
65 $questStr4 = EV2(" If $$\displaystyle \lim_{x\rightarrow x3} f(x) = 0$$ 66 and $$\displaystyle \lim_{x\rightarrow x3} g(x) = 0$$, then $$\displaystyle \lim_{x\rightarrow x3} 67 [f(x)/g(x)]$$ 68 does not exist"); 69$ansStr4 = "F";
70
71 $questStr5 = EV2(" If $$\displaystyle \lim_{x\rightarrow x3} f(x) = 0$$ 72 and $$\displaystyle \lim_{x\rightarrow x3} g(x) = a1$$, then $$\displaystyle \lim_{x\rightarrow 73 x3} [f(x)/g(x)]$$ 74 does not exist"); 75$ansStr5 = "F";
76
77 $x4 = random(1,7,1); 78$questStr6 = EV2(" If $$\displaystyle \lim_{x\rightarrow x4} [f(x)g(x)]$$ exists,
79 then the limit is  $$f(x4)g(x4)$$ ");
80 $ansStr6 = "F"; 81 82$questStr7 = EV2(" If $$p(x)$$ is a polynomial, then
83 then the limit $$\displaystyle \lim_{x\rightarrow x4} p(x)$$ is  $$p(x4)$$");
84 $ansStr7 = "T"; 85 86$questStr8 = EV2(" If $$\displaystyle \lim_{x\rightarrow x3} f(x) = \infty$$
87 and $$\displaystyle \lim_{x\rightarrow x3} g(x) = \infty$$, then $$\displaystyle \lim_{x\rightarrow 88 x3} [f(x)-g(x)] =0$$
89 ");
90 $ansStr8 = "F"; 91 92$questStr9 = EV2(" If $$f'(x4)$$ exists, then
93 then the limit $$\displaystyle \lim_{x\rightarrow x4} f(x)$$ is  $$f(x4)$$");
94 $ansStr9 = "T"; 95 96$questStr10 = EV2(" If $$f(x)$$ is continuous at $$a$$, then
97  $$f(x)$$ is differentiable at $$a$$");
98 $ansStr10 = "F"; 99 100$questStr11 = EV2(" If $$f(x)$$ is differentiable at $$a$$, then
101  $$f(x)$$ is continuous at $$a$$");
102 $ansStr11 = "T"; 103 104 @questions =($questStr1,$questStr2,$questStr3,$questStr4,$questStr5,$questStr6,$questStr7,$questStr8,$questStr9,$questStr10,$questStr11);
105 @answers =($ansStr1,$ansStr2,$ansStr3,$ansStr4,$ansStr5,$ansStr6,$ansStr7,$ansStr8,$ansStr9,$ansStr10,\$ansStr11);
106
107 ## Now choose radomly 5  questions out of the 11 question strings above.
108
109 @slice = NchooseK(scalar(@questions),5);
110
111 ## Next we output the 5 chosen questions.
112 TEXT(
113 &match_questions_list(@questions[@slice])
114 );
115