Find the Z transform of [cos (ax), x20 f(x)=: 0, x<0

Q: Find Laplace transform of x(t)=t (cos)^2 (wt)u(-2t). *

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Q: What is the initial value of f(t) if its Laplace transform is

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Q: f(t) = 3e " cosh (In 21)

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Q: Compute the Fourier Transform of f(x) = e-ax-

A: Fourier transform of a function fx is defined as  Ffx=∫-∞∞fxeisx dx Gamma function =∫0∞e-x xn-1 dx

Q: If f(x) has the Fourier transform F(p), then f(x) cos ax has the Fourier transform [F(p-a) + F(p +…

A: If Fourier transform of f(x) is F(p), then we have to prove that the Fourier transform of f(x)…

Q: The Laplace transform of f (t) = cos(2t) + 2e-3t + 3t? is: %3D

A: Note the following results : Lcos at=ss2+a2  Leat=1s-a Ltn=n!sn+1 ; n=1,2,3,…… Linearity property…

Q: Show that the Fourier transform of f (x)= e*/2 is e

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Q: Find the inverse Laplace transform of 1 F(x) S- s2 (s + 1)

A: If L[f(t)]=F(s), then f(t) is called the inverse Laplace transform of F(s).…

Q: * Find the inverse Laplace transform for-1 1 F(s) s – 2s + 5 1 -e²"sin2t 2 1,2'sin2t e'sin2t خيار 1…

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Q: Compute the Fourier transform of the following function: f(x, y) = e-()x-y|+|x+y\)&

A: The given function is, fx,y=e-x-y+x+y The two dimensional Fourier transform is defined by,…

Q: Use a Fourier transform to solve the following initial value problem for the free Schrödinger…

A: Given: Let us consider the given ut=iuxx ; ux,0=e-x2

Q: determine the inverse Laplace transform of F.

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Q: Find the Fourier cosine transform of f(x) = e-2x + 4e-3x

A: Given, f(x) = e-2x + 4e-3x Find Fourier cosine transform

Q: Find the laplace transform of f(t)=2t^2 e^-t - sin^2 t

A: We have to find the Laplace transform of f(t)=2t2e-t-sin2t .

Q: f(x)= 23, X cosx x2 x2월 욀

A: This question is for Laplace transform not for inverse Laplace.

Q: Calculate the Fourier transform of f(x) = (1 – 2)e-(z-a)?/2_

A: Calculate Fourier transform of e-x-a2/2:  ∫-∞∞e-x-a2/2·e-jωxdx=e-jaω∫-∞∞e-x-a2/2·e-jωx-adx-a…

Q: Determine the Fourier transform of f(t) = te-2t u(t), where

A: Given ft = te-2tut where ut =0     t&lt;01    t&gt;0 The Fourier transformation is given by Fw…

Q: What is the Fourier transform of the following e-j10ntx(t)

A: The Fourier transform of the function f(t) is represented as F(k), it is defined as ∫-∞∞e-jktf(t)dt,…

Q: Compute the Fourier transform of the following function: f (x, y) = e-(1x-y|+|x+y[)<+

A: Calculate Fourier transform: Fu,v=∫y=-∞∞∫x=-∞∞fx,ye-2πjux+vydxdy…

Q: * + 3x + 6x = 0, x(0) = 0, x(0) = 3, x(t) =?

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Q: What is the Laplace transform of x(t) = e-tcos(pi)t?

A: To find the Laplace transform of ,  x(t) = e-tcos πt Here the proof for standard form has been…

Q: Obtain the Fourier transform of the function where f(x) = 0 for x &lt; 0 and f(x) = e−axsin(bx) for…

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Q: Find the Fourier transform for x[t] = at*u[t], |a| &lt; 1

A: Given function is,

Q: 2. x(t) = e5t + cos 3t %3D

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Q: Find the Laplace transform of u2(t)cos(t − 2)

A: This is laplace transform shift problem

Q: Find Inverse Laplace transform of this -{in (1 + #)}' where c is a constant.

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Q: Find the fourier sine transform of a) f(x) = exp(-ar) and deduce sin(sz) -ds = 2+a² -az b) f(x)= re'…

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

Q: 3. Find the Fourier Transform of f(t) = 0, - osts0 le-at, osts ∞ a is positive constant

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Q: f(x) = = 1 2 cos: X x

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Q: 25. а. Apply Fourier transform to solve: ди for 0 < x, t 20 Under the conditions,

A: Given,              ∂u∂t=∂2u∂x2,  for  0≤x, t≥0           (1)Under the conditions,…

Q: Find the Fourier transform for f (x) xe c > 0

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Q: a) Find the finite Fourier cosine Transform of f (x) = x² in 0 < x < 4.

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Q: f (t) = cos2

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Q: Find the finite cosine transform of f (x) if ƒ (x) = -x+ in (0, t).

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Q: Give the Laplace transform of -2x 0Sx and x < 3 f(x) = 4 3<x -3s 27 20 O F(s) = -- b) O F(s) = - -3s…

A: Solution :-

Q: x (n) = sin лn u (n)?

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Q: 1.) Give the Fourier transform of the function f. Sx ha x = [0, 1] f(x) = 0 otherwise.

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Q: Calculate the Laplace transform of f(t) = 2 cos(3t)

A: The given function is ft=2 cos3t.

Q: Find the Fourier transform of f (x) defined by |x| a f (x) = sin? ax ta and hence prove that x2 2

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Q: Find the Fourier Transform F(w) = {e-at t≥0 t≤0

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Q: Solve the Laplace Transform 8. f(x) = (2/x)(cos1/2x)

A: note : We will consider the given function as : f(x) = (2/x) cos(0.5x)   Now we have to find the…

Q: Find the inverse Laplace transform of H(s) +ed

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Q: If f(x) has the Fourier transform F(p), then f(x) cos ax has the Fourier transform [F(p-a) + F(p +…

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Q: Find the finite Fourier Cosine Transform of f (x), where 0<x <"/3 when f(x) = (x – n when T/3<x<n°

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Q: 9. Solve the IVP using Laplace transform: x' – x = 2cos5t, with x (0) = = 0.

A: Given equn isx'-x=2 cos 5t with x0=0taking both the side laplace transformation we get…

Q: Find the Fourier Transform of f) = { - z - n<x< 0 0 <x<T

A: We have to find the Fourier Transform of…

Q: Find the Laplace Transform of f -1 Osx<1 f(x) = 1 x21 2e-s 1 a. 2e-s 52 1 b. 2e-s 1 C. 2e-s 1 d. +

A: We find Laplace transform of given function

Q: Find the Laplace transform of f(t) = te-t from the definition.

A: Here we use the definition of lapses transformation.