The function f(x) = sin(x) needs to be interpolated on the closed interval [0,ƒ]. (a) Does a linear interpolation, which uses the two sampling points xa = 0 and x₁ = π, make sense? Shortly justify your answer. (b) Determine the second order interpolation polynomial p2(x). For it, use the sampling points xo 0, x₁ = and x2 = π. = (c) With the help of p2(x) find an approximate solution for SC f(x)dx.
The function f(x) = sin(x) needs to be interpolated on the closed interval [0,ƒ]. (a) Does a linear interpolation, which uses the two sampling points xa = 0 and x₁ = π, make sense? Shortly justify your answer. (b) Determine the second order interpolation polynomial p2(x). For it, use the sampling points xo 0, x₁ = and x2 = π. = (c) With the help of p2(x) find an approximate solution for SC f(x)dx.
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 function f(x) = sin(x) needs to be interpolated on the closed interval [0,ƒ].
(a) Does a linear interpolation, which uses the two sampling points xa = 0 and
x₁ = π, make sense? Shortly justify your answer.
(b) Determine the second order interpolation polynomial p2(x). For it, use the
sampling points xo 0, x₁ = and x2 = π.
=
(c) With the help of p2(x) find an approximate solution for
SC
f(x)dx.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4810b3f8-7174-4e11-ad5b-d1003066dd42%2F8620fc0a-db15-4309-a626-53cc2a586dda%2F7sub4g_processed.png&w=3840&q=75)
Transcribed Image Text:The function f(x) = sin(x) needs to be interpolated on the closed interval [0,ƒ].
(a) Does a linear interpolation, which uses the two sampling points xa = 0 and
x₁ = π, make sense? Shortly justify your answer.
(b) Determine the second order interpolation polynomial p2(x). For it, use the
sampling points xo 0, x₁ = and x2 = π.
=
(c) With the help of p2(x) find an approximate solution for
SC
f(x)dx.
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