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16c_trig_problems_series - Math 160 Daddel Trigonometric...

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Unformatted text preview: Math 160 Daddel Trigonometric Power Series Problems for HW # 23. and # 23 Please do All problems Even and Odd. 1.) Use the known Maclaurin series for 6“”, sin an, cos x, , and 1n(1 +x) together with standard shortcuts (substitution, polynomial multiplication, polynomial division, differentiation, and integration) to find the first three nonzero terms of the Maclaurin series for each of the following functions. a.) emln(1+ a3) 2w+m2 b.) 1n(l — as) c.) (sin(x/3))2 6 1 e.) (1 _ 11:)4 (HINT: Start with l _ a; and use differentiation.) f("+1)(cn)($ - 00'“ (n + 1)! ’ where on is between 1' and a, to estimate the exact value of each number with error at most 0.0001 3..) 80'7 2.) Use the absolute Lagrange error (remainder) for a Taylor series, |R(m;a)| = b.) sin(1.1) c.) 1n(0.8) 3.) Write each Maclaurin series as a simple function. x m2 m3 3:4 dH—s+I—a+n“ Wigwam: . 2 3 4 5 ...
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