Question

The Fourier series of a function f(x) converges to f(x) if x is a point of

Answer

A continuity

C.O differentiability

B.O discontinuity

D.O none of these​

Answer 1

Answer:

The Fourier series of a function $f(x)$ converges to $f(x)$ if $x$ is a point of discontinuity.

Step-by-step explanation:

We know that $f(x)$ has a jump discontinuity at $x=a$, and if the limit of the function from the left, denoted $f(a^-)$, and the limit of the function from the right, denoted $f(a+)$, both exists and $f(a^-)\neq f(a^+)$.

Next, we know that $f(x)$ is piecewise smooth if the function can be broken into distinct pieces and on each piece both the function and its derivative, $f'(x)$, are continuous.

Therefore, we can say that $x$ is a point of discontinuity.