Let f(x) = cos(x x2).(a) Use a CAS to approximate the maximum value of
Chapter 7, Problem 49(choose chapter or problem)
Let \(f(x)=\cos \left(x-x^{2}\right)\).
(a) Use a CAS to approximate the maximum value of \(\left|f^{(4)}(x)\right|\) on the interval [0, 1]
(b) How large must the value of n be in the approximation \(S_{n}\) of \(\int_{0}^{1} f(x) d x\) by Simpson's rule to ensure that the absolute error is less than \(10^{-4}\)?
(c) Estimate the integral using Simpson's rule approximation \(S_{n}\) with the value of n obtained in part (b).
Equation Transcription:
∫
Text Transcription:
f(x)=cos(x-x^2)
|f^(4) (x)|
S_n
Integral^1_0 f(x) dx
10^-4
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