math231test3whitesol

# math231test3whitesol - ROW SEAT Discussion Section Family...

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ROW SEAT ———————– ——————————————– ————————— Discussion Section Family Name, First Name UIN MATH 231 Section AL1 TEST #3 WHITE 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

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MATH 231 Section AL1 TEST #3 WHITE page 2 of 5 Problem 1. Suppose the inﬁnitely diﬀerentiable function f ( x ) has X k =0 e 3 k ( x - 1) 2 k as the Taylor series expanded around 1. [4 marks] (a ) State the values of f 0 (1) and f 00 (1). Compare the ﬁrst terms of k =0 e 3 k ( x - 1) 2 k and n =0 f ( n ) (1) n ! ( x - 1) n to get f 0 (1) = 0 , f 00 (1) = 2! e 3 . [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 3 ( x - 1) 2 , P 4 ( x ) = 1 + e 3 ( x - 1) 2 + e 6 ( x - 1) 4 . [5 marks]
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## This note was uploaded on 05/20/2008 for the course MATH 231 taught by Professor Bronski during the Spring '08 term at University of Illinois at Urbana–Champaign.

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math231test3whitesol - ROW SEAT Discussion Section Family...

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