GATE ME 2022 Set 1 — Question 14
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Engineering Mathematics → Single Variable Calculus → Fourier Series
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Question
The Fourier series expansion of in the interval with periodic continuation has
Correct answer
(A) only sine terms
Solution
Let .
Check for symmetry in the interval :
.
Since , the function is an odd function.
For an odd function defined on a symmetric interval , the Fourier series coefficients and (cosine terms) are zero:
The series will only contain coefficients (sine terms):
Therefore, the expansion has only sine terms.
Check for symmetry in the interval :
.
Since , the function is an odd function.
For an odd function defined on a symmetric interval , the Fourier series coefficients and (cosine terms) are zero:
The series will only contain coefficients (sine terms):
Therefore, the expansion has only sine terms.
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