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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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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The Maclaurin series for f(x) = e^x is
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.
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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