Question

23 : Which of the following is not Dirichlet's condition
for the Fourier series expansion?
2503122659
f(x) is periodic, single valued, finite
f(x) has finite number of discontinuities in only
one period
f(x) has finite number of maxima and minima
f(x) is a periodic, single valued, finite​

Answer 1

Your Answer is ✨

f(x) is a periodic , single valued , finite [option D]

Answer 2

Given,

Which of the following is not Dirichlet's condition  for the Fourier series expansion?  

(a) f(x) is periodic, single valued, finite

(b) f(x) has finite number of discontinuities in only  one period

(c) f(x) has finite number of maxima and minima

Solution,

Know that following are the Dirichlet's conditions for the Fourier series expansion:-

(a ) f(x) must be absolutely integrable over a period.

(b) f(x) must be of bounded variation in any given bounded interval.

(c) f(x) must have a finite number of discontinuities in any given bounded interval, and the discontinuities cannot be infinite.

Hence, the correct option is (b) i.e.f(x) has finite number of discontinuities in only  one period.