MATH 129 Midterm: MATH 129 University of Arizona Exam 3C S16

• School: University of Arizona
• Department: Mathematics Main
• Course: MATH 129
• Professor: All

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[5 points] circle all solutions to the di erential equation. 5y + 6y = 0: y = e2x, y = x2, y = e3x, [5 points] suppose the taylor series about x = 1 for a function f is f (x) = What is f (4)(1): 1, 2, 4, 8, none of these, [10 points] use taylor series to nd the exact sum of the series. 3: [15 points] write out the rst four nonzero terms for the taylor series of the function for x near 0. You may use the table provided. g(x) = sin(x) 1 + x: [15 points] write out the rst ve terms of the taylor series for x centered at x = 1. Compute the terms directly from the de nition - do not use the table of known taylor series: [15 points] solve the initial value problem: dw dz.