For the set of functions {sin(x),sin(2x),sin(3x),...}=sin(nx)}, n=1,2,3,... on the interval [0,pi]. Show that the set of functions is orthogonal on [0,pi].
For the set of functions {sin(x),sin(2x),sin(3x),...}=sin(nx)}, n=1,2,3,... on the interval [0,pi...
QA: Pick two of the following functions: sin(3x)*sin(2x) cos(3x)*sin(2x) cos(3x)*sin(1x) cos(3x)*cos(2x) Find the integral of those functions from x= -pi to pi Show all work. hint : graph & use symmetry.
determine if the set is orthogonal in the interval{sen 2nx}, n = 1,2,3... [0, 7/2).
Consider the series following series of functions ' sin(nx) 3 n-1 a) Show that the series is absolutely and uniformly convergent on the real axis. Let f be its summation function n sin(nx) b) Show that f E C(R) and that 1 cos(nx) f'(x)= 2-1 c) Show that 「 f#072821) f(x)dx = k=0 Consider the series following series of functions ' sin(nx) 3 n-1 a) Show that the series is absolutely and uniformly convergent on the real axis. Let f...
1. Expand the following functions in terms of the orthogonal basis {1, sin 2nr. cos 2n on the interval (0, 1): n E Z, n > 0} 2. Expand the functions in problem i în terms of the basis {sin n z n є z,n > 0} on the interval (0, 1). 1. Expand the following functions in terms of the orthogonal basis {1, sin 2nr. cos 2n on the interval (0, 1): n E Z, n > 0} 2....
(4 points) 17. Solve the equation on the interval [0, 2x) cos 3x cos 3x + sin 3x sin 3x (6 points) 11. Use the Addition or Subtraction Formula only to find the exact value of the expression. Again, you must show your work to receive credit. a) cos b) sin 105
(1 point) Find the Fourier approximation to f(x) = x over the interval (-11, ] using the orthogonal set {1, sin , cos x, sin 22, cos 2x, sin 3%, cos 3x}. You may use the following integrals (where k > 1): | 1 dx = 27 - x dx = 0 sin(kx) dx = 1 L z sin(kx) dx = (-1)k+1 cos(kx) dx =1 L", cos(kx) dx = 0 Answer: f(2) + 2/pi sin + -2/pi + + 0...
Determine whether the given set of functions is linearly independent on the interval (−∞, ∞) f1(x) = x f2(x) = sin(x) f3(x) = sin(2x)
Determine whether the given set of functions is linearly independent on the interval (-00,00) fı(x) = xf2(x) = sin(x) $3(x) = sin(2x)
From Arfken 10.3.4 You are given (a) a set of functions un (x)--x", n = 0, 1, 2, (b) an interval (0, oo), (c) a weighting function w(x)-xe. Use the Gram-Schmidt procedure to construct the first three orthonormal functions from the set un(x) for this interval and this weighting function. 10.3.4 You are given (a) a set of functions un (x)--x", n = 0, 1, 2, (b) an interval (0, oo), (c) a weighting function w(x)-xe. Use the Gram-Schmidt procedure...
QD: Using graphs and symmetry, approximate the integral of i) sin(3x)*sin(1x) from x= -pi to pi. Ii) sin(0x)*sin(0x) from x= -pi to pi Iii) cos(0x)*cos(0x) from x= -pi to pi iv) what slightly weird thing happened?