Problem. We consider the Fourier expansion of the function f(0) = 0 in Lề(–1,1). By the...

Question

Question

Problem. We consider the Fourier expansion of the function f(0) = 0 in Lề(–1,1). By the Fourier expansion of f with respect t

Answer 1

Answer #1

Sinino) a given flo) = { (-11,0) T=20 wo 25 211 20 - 11 o flo)- to + E bn Cos (nwoo) + الاة C Sym (nw.g) nel nal 0 00 flo) lo

G=25 217 Cas (nI) -2Coj (nt) Qin n Cna 2 (in n flol -26-15h BNT Sin(no) 2 609 +1 Sin(no) nal n nal 90 Flos ĕ an jno narco nto

Answer 2

Similar Homework Help Questions

Given the function f(x) = 4x +5 defined on the interval (0, 3, denote by fe...

Given the function f(x) = 4x +5 defined on the interval (0, 3, denote by fe the even 3,3 of f extension on Find fep, the Fourier series expansion of fe плг пте ao + 2 bsin fer (x) а, COs n-1 that is, find the coefficients ao an, and bn With n> 1 ao ат W |1 l Given the function f(x) = 4x +5 defined on the interval (0, 3, denote by fe the even 3,3 of f...
(6) (This question does not relate to the above conditions.) Prove that the following system of...

(6) (This question does not relate to the above conditions.) Prove that the following system of trigonometric functions is an orthonormal system of L?(-7,7): cos no, sin ne 27 n=1,2,.. Moreover, set f(0) = 62. Write the Fourier expansion off with respect to the system of trigonometric functions in L'(-, 7). Problem 2. We define k00 Example. Let N be a null set. If u(x) = v(x) for x® N, then u(x) = v(x) a.e. Similarly, if lim uk(x) =...
Given the function f(x) -3x + 1 defined on the interval (0, 5], denote by fe the even extension o...

Given the function f(x) -3x + 1 defined on the interval (0, 5], denote by fe the even extension on [-5, 5] off. the Fourier series expansion of fe Find feF, + bn sin / - n-l that is, find the coefficients a , an , and bn , with n 1 . ao = anF Given the function f(x) -3x + 1 defined on the interval (0, 5], denote by fe the even extension on [-5, 5] off. the...

Consider the periodic function defined by 1<t0, 0<t<1, f(t)= f(t+2) f(), and its Fourier series F(t): Σ A,...

Consider the periodic function defined by 1<t0, 0<t<1, f(t)= f(t+2) f(), and its Fourier series F(t): Σ A, cos(nmi) +ΣB, sin (nπί), F(t)= Ao+ n1 n=1 (a) Sketch the function f(t) the function is even, odd or neither even nor odd. over the range -3<t< 3 and hence state whether (b) Calculate the constant term Ao Consider the periodic function defined by 1
(1 point) Find the Fourier series expansion, i.e., f(x) [an cos(170) + by sin(t, x)] n1...

(1 point) Find the Fourier series expansion, i.e., f(x) [an cos(170) + by sin(t, x)] n1 J1 0< for the function f(1) = 30 < <3 <0 on - SIST ao = 1 an = cos npix bn = Thus the Fourier series can be written as f() = 1/2
function is defined over (0,6) by f(x)={14x00<xandx≤33<xandx<6. We then extend it to an odd periodic function of...

function is defined over (0,6) by f(x)={14x00<xandx≤33<xandx<6. We then extend it to an odd periodic function of period 12 and its graph is displayed below. calculate b1,b2,b3,b4, Thanks so much A function is defined over (0,6) by 0<x and x <3 f (x) = 3<x and x < 6 We then extend it to an odd periodic function of period 12 and its graph is displayed below. 1.5 1 у 0.5 -10 5 10. 15 -1 -1.5 The function may be...

A function is defined over (0,3) by f(3) = 12 +1. We then extend it to...

A function is defined over (0,3) by f(3) = 12 +1. We then extend it to an even periodic function of period 6 and its graph is displayed below. 2 15 0.5 5 10 15 х -0.5 The function may be approximated by the Fourier series f () = ap + 01 (an cos ( 122 ) + bn sin (022)). where L is the half-period of the function. Use the fact that f(x) sin is an odd functions, enter...
1. The Fourier series expansion of the function f(x) which is defined over one period by 3_ z, f(z) = 쓸 +Σ1@n cos...

1. The Fourier series expansion of the function f(x) which is defined over one period by 3_ z, f(z) = 쓸 +Σ1@n cos nπχ +h,sin ηπΖ] is 1<zc2. Find the coefficients an r sin ax cosar x cos ar dr = We were unable to transcribe this image 1. The Fourier series expansion of the function f(x) which is defined over one period by 3_ z, f(z) = 쓸 +Σ1@n cos nπχ +h,sin ηπΖ] is 1
1. If Ea) 2. The Fourier series expansion of the function f() which is defined over one period by , 1<zc2 is f(...

1. If Ea) 2. The Fourier series expansion of the function f() which is defined over one period by , 1<zc2 is f(z) = ao + Find the coefficients an and simplify you answer. 1 z sin ax cos ar Jzcos az dz = Hint: f(x) cos(n") dz and a.-Th 3. The propagation of waves along a particular string is governed by the following bound- ary value problem u(0,t) 0 ue(8,t)0 u(x,0) = f(x) u(x,0) g(x) Use the separation of...

A function is defined over (0,6) by 0 <and I <3 f(1) = - { 3<;...

A function is defined over (0,6) by 0 <and I <3 f(1) = - { 3<; and <6 We then extend it to an odd periodic function of period 12 and its graph is displayed below. N y 1 0 -10 5 5 10 15 X The function may be approximated by the Fourier series f (t) = a0 + 1 (an cos (021 ) + bn sin ( 122 )), where L is the half-period of the function. Use...