APPM 1360 Midterm: appm1360spring2013exam3
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Instructions: books, notes, and electronic devices are not permitted. 1360/exam 3, (3) instructor"s name and (4) spring 2013 on the front of your bluebook. Also make a grading table with room for 5 problems and a total score. A correct answer with incorrect or no supporting work may receive no credit, while an incorrect answer with relevant work may receive partial credit. What is the radius of convergence: suppose that the derivatives of an unknown function f (x) at the point x = 2 are given by f (n)(2) = n2n! 2n(1 + n) for all n 0 (note that f (0)(2) = f (2)). Suppose also that |f (4)(x)| 4 for 2 x 3. (a) (10 pts. ) Write down t3(x), the 3rd order taylor polynomial of f (x) centered about the point a = 2 . (b) (10 pts. )
