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...
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 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...
0 3 and z s 6 We then extend it to an odd periodic function of period 12 and its graph is displayed below 2 y 1 -105 5 10 15 2 The function may be approximated by the Fourier series where L is the half-period of the function Use the fact that J(e) and fe)cL) are odd functions, enter the value of en in the box below f(z) cos an 0 for n 0,1,2,... Hence the Fourier series made...
f(x)=\x(-2<x<2), p = 4 for the given periodic function, what the Fourier series of f? a. an= 8 -cos(nm) 22 n' bn=0 Ob. 4 an = -COS(nn) n?? 4 bn= n2012 C. an 4 cos(nn) n272 bn=0 O d. an 4 22 [(-1)" – 1] bn=0 e. an= 4. -sin(n) n' 2 bn=0
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...
A periodic function y lxl for-r ? is shown below. x -? (1) Is this function even or odd or neither? (2) Calculate the Fourier series coefficients. Hint: Use integration by parts. . + ?4, cos(nox) + bn sin(nox) 2 ] ,f (x)- 21 where a,-J()cos(noxi, )innoxy
4. Consider the periodic function given below: f(x)-x 0 ㄨㄑㄧ (i) State its fundamental period, and sketch the function for 3 periods. (5 marks) i) Find the Fourier series of the given periodic function, and expand the series to give the first three non-zero a and b terms (15 marks) ii) Use the answer obtained in Q4(ii) and the given periodic function, find the sum of the series 4(2n-1 )2 (5 marks)
1. Consider the function defined by 1- x2, 0< |x| < 1, f(x) 0, and f(r) f(x+4) (a) Sketch the graph of f(x) on the interval -6, 6] (b) Find the Fourier series representation of f(x). You must show how to evaluate any integrals that are needed 2. Consider the function 0 T/2, T/2, T/2 < T. f(x)= (a) Sketch the odd and even periodic extension of f(x) for -3r < x < 3m. (b) Find the Fourier cosine series...
1. Cousider the followving periodic function a) Determine whether the following function is odd, even or neither f(x) = sin 2x cos 3a. 2marks] Consider the following periodic function b) ㄫㄨ for -2 < x < 0 for 0< S 2 f(x) = { sin 0 f(x) = f(x + 4). i. Sketch the graph of the function over the interval-6< r <6. 2marks] Find the Fourier Series of f(x). (6marks ii.