Question

Find bn if the function f(x) = x2
finite value
Infinite value
ОООО
zero
O Can't be foundफाइनल लेप्लास डांस फॉर्म ऑफ ए टू द पावर टू साइन ब्रैकेट बी ब्रैकेट क्लोज ​

Answer 1

Answer:

c) zero

Step-by-step explanation:

Given:- f(x) = $x^{2}$

To Find:- $b_{n}$ if the function is f(x) = $x^{2}$

Solution:-

Fourier series uses the orthogonal relationship of the sine and cosine functions. It's formula for a function is written as,

                    $f(x) = \frac{1}{2} a_{0} +$ ∑ $a_{n} cos nx$ + ∑ $b_{n} sin nx$ , where

$a_{0} = \frac{1}{\pi } \int f(x) dx$ in the interval [-π, π]

$a_{n} = \frac{1}{\pi } \int f(x) cos nxdx$ in the interval [-π, π],

$b_{n} = \frac{1}{\pi } \int f(x) sin nxdx$ in the interval [-π, π],

n = 1, 2, 3, ....

Here, we know that sin(nx) is an odd function and cos(nx) is an even function.

Since $b_{n}$ includes sin(nx) term which is an odd function and as we know odd times even function is always odd. So, the integral will give zero as the result.

A function is known as an even function if  f(−x) = f(x).

The given function is f(x) = $x^{2}$, which is an even function and even times odd function (sin(nx)) gives odd function.

Hence the coefficient in the given interval will be zero.

Hence the correct option is c) zero.

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To find the Fourier series for f(x) = xsinx, visit here

https://brainly.in/question/4939434

To find the Fourier series for f(x) = $\frac{\pi - x}{2}$ in the interval (0, 2), click here

https://brainly.in/question/14292890

Answer 2

Answer:

Step-by-step explanation:

Since in this question the interval in which the function is periodic is not given , hence the the correct answer is "CANNOT BE FOUND"