[npl] / trunk / NationalProblemLibrary / WHFreeman / Rogawski_Calculus_Early_Transcendentals_Second_Edition / 2_Limits / 2.3_Basic_Limit_Laws / 2.3.16.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

# View of /trunk/NationalProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/2_Limits/2.3_Basic_Limit_Laws/2.3.16.pg

Tue Nov 8 15:17:41 2011 UTC (18 months, 2 weeks ago) by aubreyja
File size: 1676 byte(s)
Rogawski problems contributed by publisher WHFreeman. These are a subset of the problems available to instructors who use the Rogawski textbook. The remainder can be obtained from the publisher.

    1 #Problem 2.3.16 ET2e
2
3 DOCUMENT();
4
5 # Load whatever macros you need for the problem
7            "PGbasicmacros.pl",
8            "PGchoicemacros.pl",
10            "PGauxiliaryFunctions.pl",
11            "PGgraphmacros.pl",
12           );
15
16 ## DBsubject('Calculus')
17 ## DBchapter('Limits and Derivatives')
18 ## DBsection('Calculating Limits Using the Limit Laws')
19 ## KEYWORDS('calculus', 'limits', 'basic limit laws', 'polynomial functions')
20 ## TitleText1('Calculus: Early Transcendentals')
21 ## EditionText1('2')
22 ## AuthorText1('Rogawski')
23 ## Section1('2.3')
24 ## Problem1('16')
25 ## Institution('W.H.Freeman')
26
27 $showPartialCorrectAnswers = 0; 28 TEXT(beginproblem()); 29 30$n=random(1,6,1);
31 $a=random(2,7,1); 32$b=$a+1; 33 34 BEGIN_TEXT 35 \{ textbook_ref_exact("Rogawski ET 2e", "2.3","16") \}$BR
36 Evaluate the limit using the Limit Laws: $BR 37 $$\lim\limits_{x \to n} x (x+a) (x+b) =$$ \{ ans_rule(4) \} 38 39 END_TEXT 40 41$answ=$n*($n+$a)*($n+$b); 42 43 SOLUTION(EV3(<<'END_SOLUTION')); 44$BR$BBOLD Solution:$EBOLD
45 $BR 46 We apply the Product Law and Sum Law:$BR
47 $$\lim\limits_{x \to n} x (x+a) (x+b) = \Large( \normalsize\lim\limits_{x \to n} x \Large) (\normalsize \lim\limits_{x \to n} (x+a) \Large) ( \normalsize \lim\limits_{x \to n} (x+b)\Large )\normalsize =$$ $BR $$=n \Large ( \normalsize \lim\limits_{x \to n} x + \lim\limits_{x \to n} a \Large ) ( \normalsize \lim\limits_{x \to n} x + \lim\limits_{x \to n} b \Large ) \normalsize = n (n+a)(n+b) = answ$$. 48 49 END_SOLUTION 50 51 ANS( num_cmp($answ ) );
52
53 ENDDOCUMENT();
54