Let S(h) denote the composite Simpson's rule approximation of | f(x) dæ with step size h, and suppose that f(0) = 1, f(0.25) = 5, f(0.5) = 6, ƒ(0.75) f(1) = –1. = -0.5, and a) Find the approximations S(0.5) and S(0.25).

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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4. Let S(h) denote the composite Simpson's rule approximation of / f(x) dx with step
size h, and suppose that f(0) = 1, f(0.25) = 5, f(0.5) = 6, f(0.75) = –0.5, and
f(1) = –1.
a)
Find the approximations S(0.5) and S(0.25).
1
b)
Estimate the error
| f(x)
f (x) c
dx – S(0.25)
Estimate how small h must be for S(h) to approximate the integral
c)
with an error at most 10-'.
Transcribed Image Text:1 4. Let S(h) denote the composite Simpson's rule approximation of / f(x) dx with step size h, and suppose that f(0) = 1, f(0.25) = 5, f(0.5) = 6, f(0.75) = –0.5, and f(1) = –1. a) Find the approximations S(0.5) and S(0.25). 1 b) Estimate the error | f(x) f (x) c dx – S(0.25) Estimate how small h must be for S(h) to approximate the integral c) with an error at most 10-'.
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