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Question 9 Find 5x+1 f(x) dx given that f(x) = { 3-x 0<x< 1 1<x<3 =la ole ala ala T
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
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.
find the Fourier series of f (x) defined in [-1,1], if
f(x) = ( (1 – a)x 0 5x sa { aſ1 - x) a < x <1 | -f(-x) -1 < x < 0
Given, f(x) = {x #1, 2 5x<4 4,0<x< 2 (a) Sketch the graph of f(x) and its even half-range expansion. Then sketch THREE (3) full periods of the periodic function in the interval -12 < x < 12. (6 marks) (b) Determine the Fourier cosine coefficients of Ql(a). (10 marks)
7. For the probability density function f(x) = for 0 <<<2 (a) Find P(x < 1) (b) Find the expected value. (c) Find the variance.
Q1 Given, f(x) = {x +1, 2 5x<4 4,0 < x < 2 (a) Sketch the graph of f(x) and its even half-range expansion. Then sketch THREE (3) full periods of the periodic function in the interval – 12 < x < 12. (b) Determine the Fourier cosine coefficients of Ql(a). (c) Write out f(x) in terms of Fourier coefficients you have found in Q1(b).
f(x) = 2x2 – 3, if x < 2 x2, if 2<x< 4 5x – 7, if x > 4 a) f(0) b) f(3)
Q1 Given, f(x) = {x +1, 2 5x<4 4,0 < x < 2 (a) Sketch the graph of f(x) and its even half-range expansion. Then sketch THREE (3) full periods of the periodic function in the interval – 12 < x < 12. (b) Determine the Fourier cosine coefficients of Ql(a). (c) Write out f(x) in terms of Fourier coefficients you have found in Q1(b).
(1 point) Find the flux through through the boundary of the rectangle 0 < x < 4,0 < y < 4 for fluid flowing along the vector field (x3 + 4, y cos(5x)). Flux =