Written Assignment 12

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York University *

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Mathematics

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Nov 24, 2024

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Math 138 - Spring 2023 Assignment 12 1. Use known power series representations of functions to determine the following limits: (a) lim x → 0 sin( x 2 ) − arctan( x 2 ) x 6 (b) lim x → 0 1 − e x 3 x ln(1 − x 2 ) 2. Find the sum of ∞ ∑ n =1 ( − 2) n +2 3 n ( n + 1) . You may assume the series converges without showing it. 3. Use the power series representation of 1 4 √ 1 + x to estimate 1 4 √ 1 . 1 correct to three decimal places. 4. Use series to approximate 1 / 2 Z 0 x 2 e − x 2 dx correct to three decimal places. Copyright 2023, University of Waterloo Read more about Intellectual Property and Copyright

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Written Assignment 12

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