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Tue Nov 8 15:17:41 2011 UTC (2 years, 5 months ago) by aubreyja
File size: 1626 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 # DBsubject('Calculus')
2 # DBchapter('')
3 # DBsection('')
4 # KEYWORDS('')
5 # TitleText1('Calculus: Early Transcendentals')
6 # EditionText1('2')
7 # AuthorText1('Rogawski')
8 # Section1('10.7')
9 # Problem1('58')
10 # Author('Emily Price')
11 # Institution('W.H.Freeman')
12 DOCUMENT();
13
14
15
17
21
22
24
25 #Book Values
26
27
28
29 $a = random(2, 9); 30$f = Formula("sin(x^($a)) cos(x^($a))");
31
32 $firstfoursin = Formula("x^($a) - x^(3*$a)/3! + x^(5*$a)/5! - x^(7*$a)/7!")->reduce; 33$firstfourcos = Formula("1 - x^(2*$a)/2! + x^(4*$a)/4! - x^(6*$a)/6!")->reduce; 34 35$expanded = Formula("x^($a)-x^(3*$a)/6-x^(3*$a)/2+x^(5*$a)/24+x^(5*$a)/12+x^(5*$a)/120-x^(7*$a)/720-x^(7*$a)/144-x^(7*$a)/240-x^(7*$a)/5040");
36
37 $answer = Formula("x^($a) - 2*x^(3*$a)/3 + 2*x^(5*$a)/15 - 4*x^(7*$a)/315")->reduce; 38 39 40 Context()->texStrings; 41 42 BEGIN_TEXT 43 \{ beginproblem() \} 44 \{ textbook_ref_exact("Rogawski ET 2e", "10.7", "58") \} 45$PAR
46 Find the first four non-zero terms of the Maclaurin series for $$f(x) = f$$.
47 $PAR 48 $$f(x) =$$ \{ ans_rule() \} $$+ \cdots$$ 49 END_TEXT 50 51 Context()->normalStrings; 52 53 #Answer Check Time! 54 ANS($answer->cmp);
55
56 Context()->texStrings;
57 SOLUTION(EV3(<<'END_SOLUTION'));
58 $PAR 59$SOL
60 Substituting $$x^{a}$$ in the Maclaurin series for $$\sin x$$ and $$\cos x$$, we find
61
62 $f = (firstfoursin+\cdots) (firstfourcos+\cdots)$
63 $= expanded+\cdots$
64 $= answer + \cdots$
65 END_SOLUTION
66
67 ENDDOCUMENT()