Exam 3, Fall '05

Exam 3, Fall '05 - Math 12 Exam 3 Tufts University...

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Tufts University Math 12 Department of Mathematics November 14, 2005 Exam 3 12:00-1:20 No books, notes, or calculators. Cross out what you do not want us to grade. You MUST give reasons for full credit. You are required to sign your exam book. With your signature, you pledge that you have neither given nor received assistance on this exam. 1. (14 pts) FILL IN THE BLANKS. On the first page of your bluebook, write the letters (A) through (F) that denote the questions below. Next to each let- ter write the appropriate answer corresponding to the blank in the question at hand. ANSWERS ONLY! NO PARTIAL CREDIT! If f has a power series representation at a , that is, if f ( x ) = n =0 c n ( x - a ) n , | x - a | < R then (A) The Taylor series coefficients are given by the formula c n = (B) f has a power series representation at a given by f ( x ) = , (C) valid for | x - a | < . (D) f ( x ) dx has a power series representation at a given by f ( x ) dx = , (E) valid for | x - a | < . (F) If f ( n +1) ( x ) M for | x - a | ≤ d , then the remainder R n ( x ) of the power series satisfies the inequality | R n ( x ) | ≤
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