MATH 3600 Midterm: MATH 3600 Iowa Spring15 Exam2odExam 2016
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Find the radius of convergence of the power series p n=2 ( 2)n(x 4)n n2. Circle t for true and f for false. Then we can de ne the domain of f to be (4 r, 4 + r). Suppose f (x) = an(x 4)n has a radius of convergence = r about the point 4. Then we can de ne the domain of f to be (r 4, r + 4). The radius of convergence of the power series for f (x) = is at least as large as 13. x (x2+9)(x+5) about the point x0 = 2. Let f (x) = of x (2 . Then x (x2+9)(x+5) = n=0an(x 2)n where an = f (n)(2) n! for all values. (1 + x)y + y = 0, Determine if x = 0 is an ordinary point, regular singular point or irregular singular point. ii. ) Determine the indicial equation, the roots of the indicial equation, and the recurrence.
