1. a) Find the Laplace transform for the functions below. (i) f(t)= e²¹ sin(not), n integer. (ii) ƒ(t)=Σa,t", a„¸_constant for n=0 n = 0,1,2,...

Q: Let f (x) = f₁²² sin² (t)dt. Find ƒ' (π). ○ 2π sin² (π) π sin² (7²) ○ sin² (²) ○ 2π sin² (²)

A: The given function is

Q: Differentiate f(w) = sinw + w²tan-1w

A: We have to find differentiation of given function.

Q: Find the Laplace Transform F(t)=t^2e^(10t)

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Q: LAPLACE derivative of transform                  f(t) =      {cost      t>= π/2

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Q: Find the Fourier Transforms of the indicated function: f (x) = cos x e−x^2/2

A: The given problem is to find the Fourier transform of the given function. Given function, f(x) =…

Q: Find the sine transform of a function of x which is equal to sin x for 0 <x<a and 0 for x2a.

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Q: of f (t) = t^2*sin(2t).

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Q: 9. What is the Laplace transform of f(t)=2 sin t cost* O (2/s^2)+4 O 2/(s^2+4) O 2/s^2 O 1/(s^2+4)

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Q: Find the Laplace transform F(s) of the function f(t) = e"6(t - 3) F(s) = e^(20)

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Q: Find the Laplace transform F(s)=L{f(t)} of the function f(t)=e^(−3t) cosh⁡(5t).

A: Laplace transform of the function, f(t)=cosh(at) is

Q: QI\ Find Fourier transform for: A) f(t) = U(t)sin² (3t) C) f(t) = elct sinh(bt)

A: (A)Given the function f(t)=u(t)sin2⁡(3t).Rewriting, .We know that, .The Fourier transform of f(t) is…

Q: 7.2.12 00 Let f(t) be a function on [0, a0). The Laplace transfom of f is the function F defined by…

A: We have to find Laplace transform of given function:

Q: Find the sine Fourier transform for f (x) = sin æ, x < 0,

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Q: Q3) Verify that the Fourier transform of the function [1–|x|, 1-|x|, |x|1 ƒ (x) = = { 1 + 0 is ƒ…

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Q: Use the definition of the Laplace transform to find ℒ{f(t)} for f(t) = 2e^−3t Find the domain of the…

A: The explanation of the solution as follows:

Q: Find the inverse Laplace transform f(t) = L-' {F(s)} of the function 4s + 7 F(s) s2 + 36 4s + 7 1 {…

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Q: 4) Knowing that f = f(t), using the expressions of L[f'] and L[f"], derive an expression for d'f…

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Q: f(t) = 7t² – te¬4t -s3+14s+56 -s³+14s² +224 а. F(s): с. F(s) %3D s4+4s3 s5+16s3 -s3+14s²+56…

A: We need to find the Laplace transform of ft=7t2-te-4t Now, we have the following formulas:…

Q: Determine the value of the third derivative of f at x = 1 when f(x) e(5-2x) 1. f"(1) 2. f"(1) 3. f"…

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Q: The laplace transform of f(t) = t^3 (sinh 2t − cos 2t)

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Q: Find the Laplace transform F(s) = L{f(t)} of the function f(t) = et 4h(t – 4), defined on the…

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Q: Let F be the function given by F (x) = S" (sec² (5t) – 1) dt. Which of the following is an…

A: We have given that   F(x) = ∫2x(sec2(5t)-1)dt        ...(1). And we have to find F'(x). To find the…

Q: Find the linearization at x=a and then use it to approximate f(b) 1.) f(x)=x4, a=1, b=0.96

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Q: Q3\ Determine the z transforms to the following : Z{sinh ka} *

A: I have stated the used formula in the solution.

Q: Find the inverse Laplace transform of the function F(s)= (s- 4)e^-3s/(s^3 + 4s)

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