1. Cousider the followving periodic function a) Determine whether the following function is odd, even or...
1. Determine whether the function f(x) = (x2 - 1) sin 5x is even, odd, or neither. A. Even B. Odd C. Neither 2. a). Find the Fourier sine series of the function f(x) shown below. b). Sketch the extended function f(x) that includes its two periodic extensions. TT/2 TT Formula to use: The sine series is f(x) = 6 sin NIT P where b. - EL " (x) sin " xd
(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...
(EOTIO -4 Soalan 3 (a) State w utakon sonst cach of the following function is odd, even or neither o xcos(x) cos(2x (ii) (x+5)cos 2x (iv) e'sin(3) (v) sin(2x)sin(3x) (vi) re 6 Marks/ M A periodic function f(x) is defined as Swatw fungsi berkala R) ditakrifkan sebagai) (b) Find the Fourier series of f(x) if it is neither an even nor odd function. Carikan siri Fourier hagi x)jika ia bukan fungsi genap atau ganjil (19 Marks
Sketch the function with its (a) odd periodic extension and (b) even then find the Fourier Sine and Fourier Cosine series, respectively. periodic extension, 0< x < X f(x) = -< x< 2 2 Sketch the function with its (a) odd periodic extension and (b) even then find the Fourier Sine and Fourier Cosine series, respectively. periodic extension, 0
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...
Consider a periodic function f(x) given as -7, f(x) = { - < x < 0, 0 < x <, TT – I, f(x) = f(x + 27). i) Sketch the graph of f(x) in the interval –37 < x < 37. Then, deter- mine whether f(x) is even, odd or neither. (3 marks) ii) Hence, find the Fourier series of f(x). (12 marks)
Consider the periodic function defined by 1<t0, 0<t<1, f(t)= f(t+2) f(), and its Fourier series F(t): Σ A, cos(nmi) +ΣB, sin (nπί), F(t)= Ao+ n1 n=1 (a) Sketch the function f(t) the function is even, odd or neither even nor odd. over the range -3<t< 3 and hence state whether (b) Calculate the constant term Ao Consider the periodic function defined by 1
Fourier Series for Odd Functions Recall that if f is an odd function, f(-x)f(x). An odd Fourier series has only the sine terms, and can be approximate an odd function, so Fo(x) b sinx)+b2 sin(2x)+ b, sin(3x)+. Why is there no b, term in the series F, (x)? 1. 2. Using steps similar to those outlined for even functions, develop a rule for finding the coefficients to approximate any odd function on the interval [-π, π]. 3. If f (x)sin...
3.(2 points) Determine whether the given function is periodic. If so, find its funda- mental period. (a) f(x) = 24 (b) f(x) = sin(ſx) (c) f(x) = ln x + cos x (d) f(x) = cos(65 4.(3 points) Sketch the graph of the given function defined on an interval (-0, 0) if (a) f(x) = e" for x > 0 and f(x) is an even function. (b) f(x) = {x, 0 < x < 2 (b) [(*) = 10, x=2...
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