Consider f(x) = x[x] - 1<x< 1 Is the function even? Odd? Or neither/ Expand f...
Let be a function defined by: We define by extension the odd, periodic function of period p = 2 which coincides with the function f (x) on the interval [0, 1]. Draw over the interval [−1, 3] the graph of the function towards which the Fourier series of the odd continuation of the function f (x) converges. f(x) = 1 + x2 pour 0 < x < 1.
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)
We consider an even and periodic function of period p = 6 defined by: Calculate f (17.75). Justify your answer. f(x) = 2 + e-*, pour 0 < x < 3.
Graph the function f ro -2<x<0 f(x) = +1 O 5x<1 1 1 sx<2 Find the Fourier series of fon the given interval. Give the number to which the Fourier series converges
please answer asap a) Given a periodic wave function of f(x) = max -1<x< 1 that has a period of 27. Determine if f(x) is an even or odd function b) Find Fourier Sine Transform of f(x)=e**.
We define a function by: and we suppose that f (x + 2) = f (x) for all x ∈ R. (a) Draw the graph of the function f (x) over the interval [−3, 3]. (b) Find the Fourier series for the function f (x). f(x) = { x +1 si -1 < x < 0; si 0 < x <1, 1
3. Consider the periodic function defined by -ae sin(x) 0 x < 7T f(x) and f(x) f(x2t) - (a) Sketch f(x) on the interval -37 < x < 3T. (b) Find the complex Fourier series of f(x) and obtain from it the regular Fourier series
(1 point) Find the appropriate Fourier cosine or sine series expansion for the function f(x) = sin(x), -A<<. Decide whether the function is odd or even: f(3) = C + C +
4. (a) Expand the given function in an appropriate cosine or sine series. (x) , , -1<x<0 05x< (6 marks) (b) Find the product solutions for the given partial differential equation by using separation of variables. U, +3u, = 0 (6 marks)
please include the graph 1. Expand 7T if 0 <<< f(x) = 1 if <<, in a half-range: (a) Sine series. (b) Cosine series.