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In Parseval’s relation of Half range Fourier cosine series expansion, which of the following terms doesn’t appear?

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In Parseval’s relation of Half range Fourier cosine series expansion, which of the following terms doesn’t appear?

(a) a0

(b) an

(c) bn

(d) all terms appear

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This intriguing question originated from Fourier Half Range Series topic in division Fourier Series of Engineering Mathematics

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Correct choice is (c) bn

The explanation is: In the expansion of a function in half range Fourier cosine series, only an and a0 appear. As the function is considered to be an even function, bn term becomes a null value as the integral becomes zero. So, only bn doesn’t appear in the parseval’s relation of half range Fourier cosine series.

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