4. Consider the function f(x) = ee* on [-1,1]. a) Use Simpson's Rule with n = 6 to approximate ₁₁ ee* dx. b) Given f(4)(x) = ee* (ex +7(e*)² + 6(ex)³ + (ex)4), estimate the error incurred in the approximation in a). c) Determine the number of subintervals needed to ensure that the Simpson's Rule approximation to fee* dx is accurate to within 0.001.
4. Consider the function f(x) = ee* on [-1,1]. a) Use Simpson's Rule with n = 6 to approximate ₁₁ ee* dx. b) Given f(4)(x) = ee* (ex +7(e*)² + 6(ex)³ + (ex)4), estimate the error incurred in the approximation in a). c) Determine the number of subintervals needed to ensure that the Simpson's Rule approximation to fee* dx is accurate to within 0.001.
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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![4. Consider the function f(x) = ee* on [-1,1].
a) Use Simpson's Rule with n = 6 to approximate ₁₁ ee* dx.
b) Given f(4)(x) = ee* (ex +7(e*)² + 6(ex)³ + (ex)4), estimate the error incurred in
the approximation in a).
c) Determine the number of subintervals needed to ensure that the Simpson's Rule
approximation to fee* dx is accurate to within 0.001.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbcde9fee-829a-403f-a1fa-44b86dc0b06a%2Fb513ccfe-2adc-4c68-8a97-4b4f54c487aa%2Fkjwwa14_processed.png&w=3840&q=75)
Transcribed Image Text:4. Consider the function f(x) = ee* on [-1,1].
a) Use Simpson's Rule with n = 6 to approximate ₁₁ ee* dx.
b) Given f(4)(x) = ee* (ex +7(e*)² + 6(ex)³ + (ex)4), estimate the error incurred in
the approximation in a).
c) Determine the number of subintervals needed to ensure that the Simpson's Rule
approximation to fee* dx is accurate to within 0.001.
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