5. Expand the following functions as Fourier-Legendre series: (i) f(x)=x3 x >0 x < 0 1, (ii) f(x) = lo, 5. Expand the following functions as Fourier-Legendre series: (i) f(x)=x3 x >0...
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.
Problem #5: Expand the following function in a Fourier series of period 4. fx5x27x, 0 < x < 4 Using notation similar to Problem # 2 above, (a) Find the value of co. (b) Find the function g1(n, x). (c) Find the function g(n, x). Problem #5: Expand the following function in a Fourier series of period 4. fx5x27x, 0
Find the Fourier series of the following functions in the given intervals. f(x) = r +, - <x< g(t) = { inter) 0. -T<r <0, sin(x), 0<x< 1.
kindly solve Q3 kindly solve Q4 (25 Puan) f(x)={0 0 < x <4 Expand f(x) in Fourier series. 8 3. (25 Puan) f(x)={0 0 < x <4 Expand f(x) in Fourier series. 8 3. (25 Puan) f(x)={0 0
Problem 1. Expand f(x) em 1. Expand fo) (1.0 ,-π < x < 0 0, 0<X<T in a sine, cosine Fourier series. write out a few 0, 0<x<π in sine,cosine Fourier series Write out aferw terms of the series
Need it urgently Expand the function, f(x) = x cosx in a Fourier series valid on the interval -1 <x<t. You must show the details of your work neatly.
Please explain the solution and write clearly for nu, ber 25. Thanks. 25. Approximate the following functions f(x) as a linear combination of the first four Legendre polynomials over the interval [-1,1]: Lo(x) = 1, Li(x) = x, L2(x) = x2-1. L3(x) = x3-3x/5. (a) f(x) = X4 (b) f(x) = k (c) f(x) =-1: x < 0, = 1: x 0 Example 8. Approximating e by Legendre Polynomials Let us use the first four Legendre polynomials Lo(x) 1, Li(x)...
Question 3 Fourier transform] Find the Fourier transform of the following functions. (i) f(z) = H (t-k)e-4. (ii) f(x) = 5e-4H21 (im)(xe 0, otherwise. IV) f(x) = Fourier transform Question 3 Fourier transform] Find the Fourier transform of the following functions. (i) f(z) = H (t-k)e-4. (ii) f(x) = 5e-4H21 (im)(xe 0, otherwise. IV) f(x) = Fourier transform
find fourier series of Question 3 Find Fourier series of f(x)= 0 if -55x<0 and f(x) = 1 if 0<x<5 which f(x) is defined on (-5,5).
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...