If the Fourier transform of √ 2 1 < t <3 elsewhere f(t)= {² 0 is F(w), express the Fourier transform of [12 0

Q: Find the third Maclaurin polynomial to f(x) = e sinx

A: The Maclaurin series; fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+.... Where the center is at x=a=0…

Q: Express f(x)= 4+ 6 x² + 7 x + 2 in terms of Legendre Polynomials.

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Q: Find the Fourier transform of f(x) without using the Fourier transform table. f(x) = e-l×l. (-0 <x<…

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Q: Write the first 4 terms of the Fourier-Legendre expansion of the following function. Put in the…

A: It is known that the Fourier-Legendre polynomial series for a function fx in the interval -1,1 is…

Q: Find the Fourier transform of 4x if 121 <a f(x) - o if 1x129

A: To find the Fourier transform of the function  fx=4x,  if x&lt;a0,    if x&gt;a

Q: Form the interpolating polynomial of degree k that satisfies pG) (xo) = f(G) (xo) for 0<j< k.

A: To form: The interpolating polynomial of degree k that satisfies pjx0=fjx0 for 0≤j≤k

Q: Obtain the inverse Fourier transform of TU F(w) = {cos (4w) if |w| < 4 0

A: The given problem is to find the inverse fourier transform for the given function F(w).Given F(w) =…

Q: f(x) = [sin x if 0 T

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Q: Find the finite difference formula for the second derivative at point x=x; with points X₁, Xi+1,…

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Q: Solve the fourier transform of the following functions: 2ix if-1 < x < 1 otherwise 1. f(x)= = {e²

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Q: +¹²+z111² Prove that x12 where prime denotes differentiation w.rts. = 1 p² o² + 1+p¹² P

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Q: 3. Find the Fourier transform of: (a) e-r²/2 (b) xe-2|z| (c) erfx = // Se √ Ső e-²² dz

A: As per our company guidelines, since the question has multiple subparts we will solve the first part…

Q: Compute the coefficient Fourier an of the *-1, 0<r <a S(2) = { 0, *<I< 27

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Q: 1. Find the fourth Maclaurin polynomial for f (x)= sin 2x.

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Q: Find the Fourier Cosine Transform of the function 031.png ... f(x)= (ae¯mx + hex} if x>0 -nx if a =…

A: Please check step 2 and 3 for the solution.

Q: (еxp(-ах) when |x| 1 1

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Q: -3 Compute the coefficient Fourier an of the f(x) = { -1<x<0 0<x<1

A: Apply the concept of even - odd function and very easily guess the solution.

Q: Find the Fourier approximation f2 for if -1 < x < 1/1/201 2 otherwise. f(x) f₂(x) = 0 eBook = 1 X

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Q: . Find the Fourier transform of (x if 0<x< a f(x) 0 otherwise

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Q: Verify that the Legendre polynomial Pn(x) satisfiesthe second-order equation(1 − x2)y'' − 2xy' + n(n…

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Q: (3 f(t) = - 2<t< 2 otherwise %3D

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Q: a. Find Fourier transform for the following function l(x): -1 15 |(x) = {". (Hint: \r| =r for r> 0,…

A: The given function is  l(x)=1 if -1&lt;x&lt;10  if |x|&gt;1 We know that the Fourier transform of a…

Q: Compute the Fourier Transform of the following function (3 , –n < x < o (1 , 0<x< TI f(x) =

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Q: f(x)= 0, x 1

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Q: In each of Problem, write the Fourier integral representation (14.1) of the function and determine…

A: The Fourier integral representation of a function f(x) is given by:   f(x) = (1/√(2π)) ∫[from -∞ to…

Q: Consider the following function 5z2 – 4z +3 f (2) = (z + 1) (z + 2) (z +3) Find the residue at each…

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Q: Let f(x) = (x2 + 1), n<x <a be a periodic function, then the Fourier coefficient az = Answer:

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Q: find the nth Maclaurin polynomial for the function

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Q: Q8 Find the Fourier transforms of: 0- (0 f(x) = sin² -р² <x<p² otherwise

A: Q 8. Given,                f(x)=psin2xp-pπ≤x&lt;pπ0otherwise.

Q: If the Fourier transform of f(x) is f(k): f(x) x (a) Find the Fourier transform of in terms of f(k).…

A: Given that the Fourier transform of  is .We need to find the Fourier transform of  in terms of .We…

Q: Use the definition of Fourier Transform, i.e. the equation f(t) = LF(@) elatdw to find the Fourier…

A: Using the given definition f(t) =12π∫-∞∞F(ω) e j ω tdω we have , F(ω) =12π∫-∞∞ f(t) e -j ω tdt…

Q: Show that the Fourier sine transform of the function 0 < x≤1 {:- 1-x 1 ≤ x ≤ 2 2≤x is given by 2 sin…

A: I think the given answer is not correct.

Q: Find the Fourier integral of the function f(x)= e* when x> 0 and f(-x) = f(x) for k > 0 cosix and…

A: Fourier integral, for even function

Q: 0.x 1

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Q: 8. Find the 6th order Fourier approximation of the function that is periodic and f(x) = x, -2<x <2

A: Given function is fx=x ,   -2≤x≤2 Compare the interval  -2≤x≤2 with -L≤x≤L, we get L=2…

Q: A Fourier transform is another integral transform often used in higher mathematics. The Fourier…

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