Let S5(x) represent the continuous least-squares trigonometric polynomial of degree 5 for f(x) = -x on [-, π]. Let further I(u) be I(u) = f e-x² S5(x) tanh(sinh-¹(x)) dx. If, for a certain value of u, I is approximated using the Trapezoidal rule as -0.015, then approximate that value of u by using Newton's method with an initial approximation of such that the relative error between two iteration steps is less than 10-6.
Let S5(x) represent the continuous least-squares trigonometric polynomial of degree 5 for f(x) = -x on [-, π]. Let further I(u) be I(u) = f e-x² S5(x) tanh(sinh-¹(x)) dx. If, for a certain value of u, I is approximated using the Trapezoidal rule as -0.015, then approximate that value of u by using Newton's method with an initial approximation of such that the relative error between two iteration steps is less than 10-6.
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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![Let S5(x) represent the continuous least-squares trigonometric polynomial of degree 5 for
f(x) = -x on [-, π]. Let further 1(u) be 1(u) = f e-x² S5(x) tanh(sinh¯¹(x)) dx. If, for
a certain value of u, I is approximated using the Trapezoidal rule as -0.015, then
approximate that value of u by using Newton's method with an initial approximation of
such that the relative error between two iteration steps is less than 10-6.
TL
Show Transcribed Text
please explain it.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F112fa64e-d0df-44cc-897b-72f060ba2cd5%2F12ba2adb-0d17-4403-bf93-fc1637994e79%2F1al61uf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let S5(x) represent the continuous least-squares trigonometric polynomial of degree 5 for
f(x) = -x on [-, π]. Let further 1(u) be 1(u) = f e-x² S5(x) tanh(sinh¯¹(x)) dx. If, for
a certain value of u, I is approximated using the Trapezoidal rule as -0.015, then
approximate that value of u by using Newton's method with an initial approximation of
such that the relative error between two iteration steps is less than 10-6.
TL
Show Transcribed Text
please explain it.
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