Question 3 Let f(x)be the function of period 4 which is given on the interval (-2,...
[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) be a periodic function on R with period 21. On the interval (-11,), f(x) is given by f(x)=sin(x) 0<x51, = Let F(x) be the Fourier series of f(x). Select all correct statements from below. The Fourier series of -f (x) is -F(x). F(-1) = 0.
Let f be the function of period 6 such that F(x) = ch that Fx10-35x< ch that X, OSX<3 (a) Sketch the graph of F on the interval (-6, 6]. At which points in this interval is f discontinuous? (b) Find the Fourier series of f on the interval (-3,3]. What is the value of the constant term in the series expansion? What is the value of the coefficient a? What is the value of the coefficient bz? (c) To...
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. Let f(x) be the 2T-periodic function which is defined by f(xcos(x/4) for -<< (a) Draw the graph of y = f(x) over the interval-3r < x < 3π. Is f continuous on R? (b) Find the trigonometric Fourier Series (with L = π) for f(x). Does the series converge absolutely or conditionally? Does it converge uniformly? Justify your answer. (c) Use your result to obtain explicit values for these three series: and , and 162 16k2-1" 16k2 1)2 に1...
4. Let f(x) = 6-2x, 0<x 2 (a) Expand f(x) into a periodic function of period 2, ie. construct the function F(x), such that F(x)-f (x), 0xS 2, and Fx) F(x+2) for all real numbers x. (This process is called the "full-range expansion" of f(x) into a Fourier series.) Find the Fourier series of Fr). Then sketch 3 periods of Fx). (b) Expand fx) into a cosine series of period 4. Find the Fourier series and sketch 3 periods (c)...
Let f(x) be the 27-periodic function which is defined by f(x)-cos(x/4) for-π < x < 1. π. (a) Draw the graph of y f(x) over the interval-3π < x < 3π. Is f continuous on R? (b) Find the trigonometric Fourier Series (with L π) for f(x). Does the series converge absolutely or conditionally? Does it converge uniformly? Justify your answer. (c) Use your result to obtain explicit values for these three series: 16k2 1 16k2 1 (16k2 1)2 に1...
Find a Fourier Series which converges to the following function on the interval (0,2). 2 f(z) = { x € [0, 1] 1 x € (1, 2] On the interval [-2, 2), draw the function to which your Fourier Series converges to.
Consider the function f(x) with period 4 which has f(x) = 1, -2<< -1, 0, -1<x< 1, -1, 1<x< 2. a) Sketch the function f(x) in the interval (-2,2] b) Calculate the Fourier Series for f(x). Circle your answer. c) What values does the series converge at the points x=-1 and x=1. Circle your answer.