Suppose that f(t) is periodic with period [-n, 7) and has the following real Fourier coefficients:a1 = 1,b1an = 4,a2 = 3, az = 3,2, b, =-3, bz = 0,(A) Write the beginning of the real Fourier series of f(t) (through frequency 3):f(t) =(B) Give the real Fourier coefficients for the following functions:(i) The derivative f' (t), a1 =a2 =-6az =b1 =, b2 =-6b3 =(ii) The function f(t) – 2, a1 =, a2 = 3, az =3b, =, b2 =, b3 =(iii) The antiderivative of (f(t) – 2) (with C0)an =, a1 =, a23/2, аз —b, =b2 = 3/2, b3 =(iv) The function f(t) + 3 sin(3t) +3 cos(2t)an =, a1 = 1, a2 = 6, az = 3b, = 2, b2 = -3bz =3(iv) The function f(2t)an =, a1 =, a2 =, аз —b1 =b2 =bz = 0

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Suppose that f(t) is periodic with period [-a, *) and has the following real Fourier coefficients: ao = 4, a1 = 1, az = 3, az = 3, b = 2, by = -3, by = 0, .. (A) Write the beginning of the real Fourier series of f(t) (through frequency 3): f(t) (B) Give the real Fourier coefficients for the following functions: (1) The derivative '(t) -6 b, = b = -6 b = (1) The function f(t) – 2 ag = .... b, = , b = by = (iii) The antiderivative of (f(t) – 2) (with C = 0) 3/2 az = b, = by= 3/2 by %3D (iv) The function f(t) + 3 sin(3t) + 3 cos(2t) do 1 , ds = 3 .... b, =2 b2 =-3 3 (iv) The function /(2t) , ag = bz =

Suppose that f(t) is periodic with period [-a, *) and has the following real Fourier coefficients: ao = 4, a1 = 1, az = 3, az = 3, b = 2, by = -3, by = 0, .. (A) Write the beginning of the real Fourier series of f(t) (through frequency 3): f(t) (B) Give the real Fourier coefficients for the following functions: (1) The derivative '(t) -6 b, = b = -6 b = (1) The function f(t) – 2 ag = .... b, = , b = by = (iii) The antiderivative of (f(t) – 2) (with C = 0) 3/2 az = b, = by= 3/2 by %3D (iv) The function f(t) + 3 sin(3t) + 3 cos(2t) do 1 , ds = 3 .... b, =2 b2 =-3 3 (iv) The function /(2t) , ag = bz =

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Suppose that f(t) is periodic with period [-n, 7) and has the following real Fourier coefficients:
a1 = 1,
b1
an = 4,
a2 = 3, az = 3,
2, b, =
-3, bz = 0,
(A) Write the beginning of the real Fourier series of f(t) (through frequency 3):
f(t) =
(B) Give the real Fourier coefficients for the following functions:
(i) The derivative f' (t)
, a1 =
a2 =
-6
az =
b1 =
, b2 =
-6
b3 =
(ii) The function f(t) – 2
, a1 =
, a2 = 3
, az =
3
b, =
, b2 =
, b3 =
(iii) The antiderivative of (f(t) – 2) (with C
0)
an =
, a1 =
, a2
3/2
, аз —
b, =
b2 = 3/2
, b3 =
(iv) The function f(t) + 3 sin(3t) +3 cos(2t)
an =
, a1 = 1
, a2 = 6
, az = 3
b, = 2
, b2 = -3
bz =
3
(iv) The function f(2t)
an =
, a1 =
, a2 =
, аз —
b1 =
b2 =
bz = 0

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