1. Consider e for all z € R. n=0 a. Determine the power series representation of f(x) = re-5² for all a € R. b. By first differentiating the power series in (a), determine the exact value of (-1)+¹(2n+1) n! n=0 c. Find f(23) (0). No need to simplify your answer.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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1. Consider e =[# for all z € R.
n=0
a. Determine the power series representation of f(x) = re-5² for all r € R.
b. By first differentiating the power series in (a), determine the exact value of
Σ
(-1)^²+¹(2n +1)
n!
n=0
c. Find f(23) (0). No need to simplify your answer.
2. Find the second degree Taylor polynomial of g(x) = 31-3r about 3, then use it to approximate
the value of 3-9.2. Express the estimated value in decimal form.
Transcribed Image Text:1. Consider e =[# for all z € R. n=0 a. Determine the power series representation of f(x) = re-5² for all r € R. b. By first differentiating the power series in (a), determine the exact value of Σ (-1)^²+¹(2n +1) n! n=0 c. Find f(23) (0). No need to simplify your answer. 2. Find the second degree Taylor polynomial of g(x) = 31-3r about 3, then use it to approximate the value of 3-9.2. Express the estimated value in decimal form.
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