Problem 1. Expand f(x) em 1. Expand fo) (1.0 ,-π < x < 0 0, 0<X<T...
Problem 1 Expand the periodic functions (defined on the interval T. In a sine cosine ouer seres. (a) f(x) = (1+r) for-r < x < π f(x) for 0 -π<x < 0 for sinx 0<x<π = (c) f(x) ez for-r < x < π
Expand the given function in an appropriate cosine or sine series f(x) = 1x1, -π <x<π F(x) = sin nx cos nx + n=1L Suhmit Answor Savo Drogroso
please include the graph 1. Expand 7T if 0 <<< f(x) = 1 if <<, in a half-range: (a) Sine series. (b) Cosine series.
1. Find the complex Fourier series of the following f(x) = x, -π < x < π
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 11.5. Find the Fourier cosine series of the function f(x): f(x) = 1 +X, 0 < x < .
Problem 2 x < π; f(x)-x-2π when π Function f(x) =-x when 0 f(x + 2π) = f(x). x < 2π. Also 1. draw the graph of f(x) 2. derive Fourier series
2. Let f(x) = 8 + 3x4 -1 5x<1, f(x+2) = f(x). Which best describes the Fourier series of f: (a) It is a Fourier cosine series. (b) It is a Fourier sine series. (c) It is a general Fourier series with sine and cosine terms.
please answer both questions 3. A function f(t) defined on an interval 0 <t<L is given. Find the Fourier cosine and sine series of f. f() = 6(1-1),0 <t< 4. Find the steady state periodic solution, *xp(t) of the following differential equation. *" + 5x = F(t), where FC) is the function of period 2nt such that F(t) = 18 if 0 << < 1 and F(t) = -18 if t <t <200.
Problem 6: Find the cosine series for the symmetric (even) extension (or "cosine half-range expansion") f (t) of the function g(t) by using the complex Fourier series and the method of jumps f(t) = g(t) = sin t , g(-t) =-sin t , 0<t<π [Vol.III-Ch.1, 6 -r < t < 0