Dear I am struggling with this question could you please provide a detailed answer, I will rate it. Thank you
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Dear I am struggling with this question could you please provide a detailed answer, I will...
Dear I am struggling with this question could you please provide a detailed answer, I will rate it. Thank you Consider the following periodic function f(x) with period 2. 9. a) f(x)= x. f(x)= f(x + 2) Sketch this periodic function in the interval -3sxs3 Find the Fourier series expansion of this function b) c) State the value f(0) and use it to show that (2m+1) By differentiating the series for f(x), find the Fourier series expansion of d) period...
I am struggling very much with this question, could you please provide a detailed answer, I will rate it. Thank you very much. |(a) Differentiate the following functions with respect to and simplify your answer 1. possible far as as -5 1 mark (ii) esin (2r [4 marks 11 y = In(a) [5 marks (b) Determine the following da : sin (i) 6 marks dx 11 - 1)(x +3) |(a) Differentiate the following functions with respect to and simplify your...
I am struggling very much with this question, could you please provide a detailed answer, I will rate it. Thank you very much. 4. () Show that 5 (>0) +3- 16 128 6 mar (ii Find an approximation for da by using the series of part (i) and giving your answer correct to 4dp 6 mar J(1+e d (iii) Find an approximation for by using Simpson's rule with eight equal intervals and working to 4dp. 8 mar 4. () Show...
5. (a) (6) Carefully sketch the odd periodic extension, of period 2m, of the function f(x)1, 0 < x < π. (Only sketch over the interval z E [-2π, 2π). (b) (10) Find the Fourier sine series of the function in part (a) 5. (a) (6) Carefully sketch the odd periodic extension, of period 2m, of the function f(x)1, 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...
Hi, could you please provide a clear and detailed worked solution for the following problem. Please only answer if you are 100% sure you can answer the question correctly and have neat hand writing that is easy to read. I will leave feedback that reflects the quality and completness of your answer. Thank you A periodio function f (t) is defined on its peniool oy the formula - sin t 2 2 present tme funchan by the Fourner señes using...
(a) Determine algebraically whether the functions below are even, odd or neither. i. r+6 f(x)=- r-r? (2 marks) ii. f(x) = 2x sinx (2 marks) (b) A periodic function is defined by: f(x) = 4-x?, -25x52, f(x+4)= f(x) i. Sketch the graph of the function over -10<x<10. (4 marks) ii. Based on result in (i), identify whether the function is even or odd. Give your reason. (2 marks) ii. Calculate the Fourier series expansion of f(x). (12 marks) (c) An...
I am having trouble with this linear algebra question. Any help would be greatly appreciated. QUESTION 10: Throughout this question f : R → R will denote the periodic extension (with period 2) of the function if z e [0, 1) f.: [0, 2]-→ R : x → f(x) ={2-r if re[1, 2] Do the following (a) Sketch the graph of f. 3 marks (b) Find a formula for f(t) that is valid for all t e I-1, 1]. Give...
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)...
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)