1. [8] Given x + 2, -2 < x < 0 f(x) = 12 – 2x, 0<x< 2, f(x + 4) = f(x) (a)[3] Sketch the graph of this function over three periods. Examine the convergence at any discontinuities (b)[5] Find the Fourier series of f(x) 2.[10]For the function, f(x), given on the interval 0 < x <L (a)[4] Sketch the graphs of the even extension g(x) and odd extension h(x) of the function of period 2L over three periods...
2, (a) Expand f(x) = 8, 0 < x < 3, into a cosine series of period 6. (b) Expand f(x) 8, 0<x3, into a sine series of period 6. (c) For each series, determine the value to which the series converges to when x (d) Graph the sine series in part (b) for 3 periods, over the interval [-9, 9] 42. 2, (a) Expand f(x) = 8, 0
[EUM 114 1. Let f(x) be a function of period 2 (a) over the interval 0<x<2 such that f(x) = - f(x)pada selang Diberikan f(x) sebagai fungsi dengan tempoh 2t yang mana 0<x<2m Sketch a graph of f (x) in the interval of 0 <x< 4 (1 marks/markah) Demonstrate that the Fourier Series for f(x) in the interval 0<x< 2n is (ii) 1 2x+-sin 3x + 1 sin x + (6 marks/markah) Determine the half range cosine Fourier series expansion...
Let f(x) = x.a) Expand f(x) in a Fourier cosine series for 0 ≤ x ≤ π.b) Expand f{x) in a Fourier sine series for 0 ≤ x < π.c) Expand fix) in a Fourier cosine series for 0 ≤ x ≤ 1.d) Expand fix) in a Fourier sine series for 0 ≤ x < 1.
2. [10]For the function, f(x), given on the interval 0 <x<L (a)[4] Sketch the graphs of the even extension g(x) and odd extension h(x) of the function of period 2L over three periods (b)[6] Find the Fourier cosine and sine series of f(x) f(x) = 3 - x, 0<x<3
2.[10]For the function, f(x), given on the interval 0 < x <L (a)[4] Sketch the graphs of the even extension g(x) and odd extension h(x) of the function of period 2L over three periods (b) [6] Find the Fourier cosine and sine series of f(x) f(x) = 3 - x 0<x<3
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...
Let f(x) = 1, 0 〈 x 〈 π. Find the Fourier cosine series with period 2T. Let f(x) = 1, 0 〈 x 〈 π. Find the Fourier sine series with period 2T.
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)
3. Consider the function defined by f(x) = 1, 0 < r< a, | 0, a< x < T, where 0a < T (a) Sketch the odd and even periodic extension of f (x) on the interval -3n < x < 3« for aT/2 (b) Find the half-range Fourier sine series expansion of f(x) for arbitrary a. (e) To what value does the half-range Fourier sine series expansion converge at r a? [8 marks 3. Consider the function defined by...