Σo (+) = 1 + x + ² + +... a) Use that fact to find the Maclaurin series of g(x) = e-7. b) Then use that series to evaluate the integral Set at least the first five terms. (Hint: integrate term-by-term) c) Create a polynomial function using those first five terms you found in part (b) and use Ledx to five decimal places. (Hint: just apply it to approximate the integral: the FTC to that antiderivative) dx as an infinite series. Show d) Find the percent error of your approximation given the actual integral, rounded to L₁e - 2² five decimal places is: 2 dx= 1.71125.
Σo (+) = 1 + x + ² + +... a) Use that fact to find the Maclaurin series of g(x) = e-7. b) Then use that series to evaluate the integral Set at least the first five terms. (Hint: integrate term-by-term) c) Create a polynomial function using those first five terms you found in part (b) and use Ledx to five decimal places. (Hint: just apply it to approximate the integral: the FTC to that antiderivative) dx as an infinite series. Show d) Find the percent error of your approximation given the actual integral, rounded to L₁e - 2² five decimal places is: 2 dx= 1.71125.
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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The Maclaurin series for f(x) = e^x is
Transcribed Image Text:Σo (+) = 1 + x + ² + + ...
a) Use that fact to find the Maclaurin series of g(x) = e 2.
b) Then use that series to evaluate the integral
Set
at least the first five terms. (Hint: integrate term-by-term)
dx as an infinite series. Show
c) Create a polynomial function using those first five terms you found in part (b) and use
it to approximate the integral: Ledx to five decimal places. (Hint: just apply
the FTC to that antiderivative)
d) Find the percent error of your approximation given the actual integral, rounded to
five decimal places is:
L₁e-
2 dx= 1.71125.
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