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Unformatted text preview: ROW & SEAT ———————– ——————————————– ————————— Discussion Section Family Name, First Name UIN MATH 231 Section AL1 TEST #3 YELLOW April 21, 2008 Page 1 of 5 INSTRUCTIONS Show ALL work on these pages. You may use the backside of the page if you need more room for your answer. You are allowed 50 MINUTES to complete this test. Calculators are NOT permitted. THIS PART IS FOR EXAMINER’S USE ONLY Question Marks Grade 1 13 2 6 3 6 4 10 5 15 Total 50 MATH 231 Section AL1 TEST #3 YELLOW page 2 of 5 Problem 1. Suppose the infinitely differentiable function f ( x ) has ∞ X k =0 e k ( x 3) 2 k as the Taylor series expanded around 3. [4 marks] (a ) State the values of f (3) and f 00 (3). Compare the first terms of ∑ ∞ k =0 e k ( x 3) 2 k and ∑ ∞ n =0 f ( n ) (3) n ! ( x 3) n to get f (3) = 0 , f 00 (3) = 2! e 1 . [4 marks] (b ) Determine the Taylor polynomials P 2 ( x ) and P 4 ( x ) for the given Taylor series. Read off from the given Taylor series: P 2 ( x ) = 1 + e ( x 3) 2 , P 4 ( x ) = 1 + e ( x 3) 2 + e 2 ( x 3) 4 ....
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 Spring '08
 Bronski
 Math, Calculus, Derivative, Taylor Series, Section AL1 TEST

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