Question

At the point of discontinuity, sum of the series is equal to ___________

(a) \(\frac{1}{2} [f(x+0) – f(x-0)] \)

(b) \(\frac{1}{2} [f(x+0) + f(x-0)] \)

(c) \(\frac{1}{4} [f(x+0) – f(x-0)] \)

(d) \(\frac{1}{4} [f(x+0) + f(x-0)] \)

This question was posed to me by my college director while I was bunking the class.

My question is from Fourier Series Expansions topic in division Fourier Series of Engineering Mathematics

Answer 1

Right option is (b) \(\frac{1}{2} [f(x+0) + f(x-0)] \)

The best I can explain: When there is a point of discontinuity, the value of the function at that point is found by taking the average of the limit of the function in the left hand side of the discontinuous point and right hand side of the discontinuous point. Hence the value of the function at that point of discontinuity is \(\frac{1}{2} [f(x+0) + f(x-0)] \).