Write the function below in terms of the Fourier Trigonometric Series: f(x) = 6x – 1, -1

Q: Find the Fourier series for the given function. x +L, f(x) = L. -L < x < 0, 0 <x < L; fx +2L) = f(x)

A:

Q: Q4. Find the Fourier sine series for the function: f(x)= 0 for 0<x< 1/1 for 1/1/1<x<

A:

Q: Q2 (a) Explain the difference between even and odd Fourier series function.

A: First of, we know about Odd numbers are : 1,3,5,7,….. Even numbers are: 2,4,6,8,…..   =&gt;…

Q: Use the series representation of the function f to find limx→0 f (x), if it exists.

A: The question is taken from the calculus in which we have to find the limit of given function We…

Q: For f(x) = |x| find the coefficients from the Fourier series of f(x) on the interval (-n,1) by using…

A: According to the given information, it is required to find the coefficients of the fourier series…

Q: Find the Fourier series to represent the function f(x) sin x, -I < x < T.

A:

Q: Find the Fourier series of the function 0 < x < ™, 0, -7 < x < 0. 1, f(x)

A:

Q: Calculate the Fourier series for the following function F(x)= 5x

A: Recall this

Q: Find the Fourier series on the given interval f (x) = x?,-1 <x <1

A:

Q: Find the Fourier series for the Function f(x) = 4- X2 ,When -2<X< 2

A: Period is 2-2=4. Fourier series will be: fx=ao+∑n=1∞ancosπnx2+bnsinπnx2

Q: Find the Fourier Sine series of the function f(x) = cos(x) for x e [0, T]

A: Given : f(x) = cos (x)  for x€[0,π]

Q: 一Tく*<0 f(x): (x-1, u+1,

A:

Q: ". Expand the function f(x)=|x, - T < x < A in an appropriate cosine or sine series.

A: Given that, fx=x ,  -π&lt;x&lt;π  Here, -L , L=-π,π Hence, L=π As the given function is even…

Q: Find the fourier series to represent the function f(x) sinx,-n<x<л

A:

Q: Determine the half range Fourier Cosine Series for the function f(t) = sin t 0st2

A: Consider the given information. ft=sint , 0≤t≥π2 The Fourier series is defined as,…

Q: Determine the Fourier Series of the function f(x)= |x|, -3 ≤ x ≤ 3, f(x) = f(x+6).

A:

Q: Find the Fourier series of the function -1 for - π<χ < | f (x) = for < x < - TC + 1 for < x < T.

A:

Q: Find the Fourier series representation of the periodic function below f(x) = ax? + b if -«x < 1 if a…

A:

Q: Find the Fourier series approximation of the following functions: f(x) = } S-x,(-1<x < 0) x, (0 < x…

A: Given function: fx=-x-1&lt;x&lt;0x0&lt;x&lt;1 Fourier series is given by…

Q: Find the Fourier series associated with the given functions S2. l-x, f(x) :

A:

Q: If f(t)= e^iwt at the interval (-π, π) determine fourier series of the f(t) ?

A: Given that the function ft=eiwt ,-π≤t≤π

Q: iii. f (x) -sin(2x) , -π < x < π

A:

Q: For f(x) = 4 on (0,t), find the Fourier sine series of f(x). Make sure to write the series.

A:

Q: Find the Fourier series of the given function f (x), which is assumed to have the period 2Tt. Show…

A:

Q: Write down the Fourier series for an odd function f(x) such that f(x + 2π) = f(x).

A:

Q: Write the Fourier series of the function f (x) and calculate f (10) by taking the first three terms…

A:

Q: ct the Fourier series for the function f(x) = (T-x)² for 0 <x < 2n ? %3D

A:

Q: 0, f(x) = { -T< x <0 0 <x <T

A: Concept:

Q: Find the Fourier series of the function f.

A:

Q: Find the Fourier sine series of the function f(x) = x² cos x on the interval [-L, L].

A:

Q: Find the Fourier series representation of the periodic function below f(x) = ax2 + b if -n< x < n if…

A:

Q: Given f(x) = x² ,0 < x < 3, a) sketch the function during the period. b) Express f(x) as a…

A:

Q: Sketch the odd and even extension for given function below. Then find the Fourier sine series for…

A:

Q: Find the Fourier series of the given function f (x), which is assumed to have the period 2p . f(x) =…

A:

Q: Find the half-range sine series for the function f(t)=nt-t², in the interval 0<t<n.

A:

Q: Obtain the Fourier series of function where f(x+2)=f(x) 0<x<1 f (x) 2-X 1<X<2

A:

Q: pand f(x) =5x as a half-range Fourier sine series in the range 0 < x <A , and sketch the function…

A:

Q: Find the Fourier series of the function f(x) = 4x2r², -π≤x≤T

A:

Q: Let f(x)=1-x on the interval [0;1]. Find the Fourier Sine series of f(x).

A: Fourier Series of 1-x2 on the interval 0, 1Fourier sine series of function fx on interval -L≤ x≤ L…

Q: viii. f (x) = cos(x), - 3 < x < 3

A:

Q: (1 — х, – x, for – 1< x < Ó х. f(x) = {* 0, for 0 < x < 1

A:

Q: i. f (x) = 1 – |x|, - 2 < x < 2

A:

Q: Find the Fourier series of the given function f(x) 2 f(x) = x2 (-T < x < T)

A: Fourier series for f(x)=x2, -π&lt;x&lt;π is given by f(x)=a02+∑n=1∞ancosnx+bnsinnx…

Q: …) Find the half-range sine series for the function f(t) = πt - t², in the interval 0<t<π.

A:

Q: Q3 Find the half-range Fourier cosine series of f(x) = (1 - x)" in the interval (0, n).

A:

Q: Find the Fourier series of the function f(x)={A,0≤x≤L0,L&lt;x≤2L

A:

Q: Find the Fourier series representation of the even extension of the function represented by the…

A: Here we have to find function .and then need to use Fourier series for even extension  Fourier…

Q: Represent the function below as Fourier Series: y 1 -1

A: The graph of the function is given below At θ=0, function value is 0 and when θ is π2, function…