- #1
standardflop
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A odd 2pi periodic function, for which [itex] x \in [0;\pi] [/itex] is given by [itex] f(x)=\frac \pi{96}(x^4-2\pi
x^3+\pi^3x) [/itex]
was found to have the Fourier series
[tex] f(x) = \sum_{n=1}^\infty \frac{\sin(2n-1)x}{(2n-1)^5}, \ x \in \mathbb{R} [/tex]
The problem is now: prove that [itex] |f(x) - \sin x| \leq 0.01, \forall x \in \mathbb{R} [/itex]. The hint given was: Use integral test.
x^3+\pi^3x) [/itex]
was found to have the Fourier series
[tex] f(x) = \sum_{n=1}^\infty \frac{\sin(2n-1)x}{(2n-1)^5}, \ x \in \mathbb{R} [/tex]
The problem is now: prove that [itex] |f(x) - \sin x| \leq 0.01, \forall x \in \mathbb{R} [/itex]. The hint given was: Use integral test.
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