PROBLEMS: 1. Let F(2) = * dt. Compute F(1) with 3 correct digits after the decimal point. (a) Derive MacLaurin series for e". Find its radius of convergence. (b) Using the previous point, find the MacLaurin series for e-². What is its radius of conver- gence? (c) By integrating term by term the series from the previous point, find the series for F(x). What its radius of convergence? (d) How many terms of the found in the previous point series you need to take to compute F(1) with 3 correct digits after the decimal point? Hint: Alternating series test. (e) Compute the required F(1).
PROBLEMS: 1. Let F(2) = * dt. Compute F(1) with 3 correct digits after the decimal point. (a) Derive MacLaurin series for e". Find its radius of convergence. (b) Using the previous point, find the MacLaurin series for e-². What is its radius of conver- gence? (c) By integrating term by term the series from the previous point, find the series for F(x). What its radius of convergence? (d) How many terms of the found in the previous point series you need to take to compute F(1) with 3 correct digits after the decimal point? Hint: Alternating series test. (e) Compute the required F(1).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![PROBLEMS:
1. Let
(=) = ] -
e* dt.
Compute F(1) with 3 correct digits after the decimal point.
(a) Derive MacLaurin series for e". Find its radius of convergence.
(b) Using the previous point, find the MacLaurin series for e. What is its radius of conver-
gence?
(c) By integrating term by term the series from the previous point, find the series for F(x).
What its radius of convergence?
(d) How many terms of the found in the previous point series you need to take to compute
F(1) with 3 correct digits after the decimal point? Hint: Alternating series test.
(e) Compute the required F(1).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70fd8e81-3072-448b-b01c-d8028dd2bc3f%2F78af8eeb-2ba9-4c54-99e1-f588b3f9ef79%2Fegzffde_processed.png&w=3840&q=75)
Transcribed Image Text:PROBLEMS:
1. Let
(=) = ] -
e* dt.
Compute F(1) with 3 correct digits after the decimal point.
(a) Derive MacLaurin series for e". Find its radius of convergence.
(b) Using the previous point, find the MacLaurin series for e. What is its radius of conver-
gence?
(c) By integrating term by term the series from the previous point, find the series for F(x).
What its radius of convergence?
(d) How many terms of the found in the previous point series you need to take to compute
F(1) with 3 correct digits after the decimal point? Hint: Alternating series test.
(e) Compute the required F(1).
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