Consider the following Maclaurin Series Expansion of the exponential function e x² 2:3 3! 2n t... n! For this sequence, assume x = 0.32 and the true value of e0.32 = 1.3771. e = 1 + x + + 1. Find the approximate value of e* using only the first two terms in the series i.e. 1 + x and enter the value below. Please answer with four digits after decimal. Please do not round your answer. If your answer is 2.1 then write this as 2.1000. 2. What is the value of the true relative error in %. Enter the value in the space below. Please answer with four digits after the decimal. Please do not round your answer. 3. What is the value of the approximate relative error in %. Please answer with four digits after the decimal. Please do not round your answer.
Consider the following Maclaurin Series Expansion of the exponential function e x² 2:3 3! 2n t... n! For this sequence, assume x = 0.32 and the true value of e0.32 = 1.3771. e = 1 + x + + 1. Find the approximate value of e* using only the first two terms in the series i.e. 1 + x and enter the value below. Please answer with four digits after decimal. Please do not round your answer. If your answer is 2.1 then write this as 2.1000. 2. What is the value of the true relative error in %. Enter the value in the space below. Please answer with four digits after the decimal. Please do not round your answer. 3. What is the value of the approximate relative error in %. Please answer with four digits after the decimal. Please do not round your answer.
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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Question
3
Transcribed Image Text:Consider the following Maclaurin Series Expansion of the exponential function e
e² = 1 + x +²¹² +21 +
xn
n!
For this sequence, assume x = 0.32 and the true value of e0.32 = 1.3771.
+
1. Find the approximate value of e* using only the first two terms in the series i.e. 1 + x and enter the value below.
Please answer with four digits after decimal. Please do not round your answer. If your answer is 2.1 then write this as
2.1000.
2. What is the value of the true relative error in %. Enter the value in the space below. Please answer with four digits
after the decimal. Please do not round your answer.
3. What is the value of the approximate relative error in %. Please answer with four digits after the decimal. Please do
not round your answer.
Expert Solution
Step 1
Q-1 The Maclaurin Series Expansion
x=0.32
The approximate value of using only the first two terms in the series 1+x=1+0.32=1.3200
Q-2
The true value of
The true relative error in percentage =
=
The true relative error in percentage is 4.1463%
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