Apply (3) to establish the formula for the Laplace transform of an integral, F(p) L|f(x)dx 1. and verify this by finding 1 L-1 [P(p+1)_

Q: Solve for the laplace transform x(t)= (cosh4t sin4t)/ (te6t)

A: The given function is x(t)=cosh 4t sin 4tt e6t=cosh 4t sin 4tte-6t

Q: Use the Laplace transform to solve the difference equation 3x(t) — 4x(t − 1) = 1, x(t)=0 for t < 0.

A: Given: The difference equation, 3xt-4xt-1=1, xt=0 for t&lt;0   To solve: The given difference…

Q: Find the Laplace transform of: (a) cosh at (b) sinh at

A: Given (a)cosh at  and (b)sinh at We have to find the Laplace transform of them…

Q: f(t) = {, - 2 2 -2

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Q: Apply the theorem of integration of transforms to find the Laplace transform of f(t)=2sin5t. Show…

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Q: Find the Fourier sine expansion of f(x)=x² (3L– 2x) on [0, L].

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: using con |' 1 P+ (1)

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Q: Please find the Laplace transform of et for t > s

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Q: The Laplace transform of x(t) is X(s). Given x(0)=2 and x'(0)=-1, write an expression for the…

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Q: 3 3 e. f(t) 5 sin2t *cos2t e-'cos2t - 10

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Q: a) Find the Laplace transform of f(t) = |t – 1|+|t +1|, t 2 0 [Dec 2016] r(1) = (S - b) Find the…

A: 4(a) The given function is f(t)=t-1+t+1;  t≥0 so, it will be  f(t)=2    if t&lt;12t   if t≥1 taking…

Q: | (t – cos(3t))e-'dt

A: Using definition of Laplace transform.

Q: Evaluate the Laplace transform of f(1) = { ; 0≤t <% cost ; t≥% 0

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Q: S(1) = >1

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Q: Use the definition of Laplace transform to find L{f}. (Do the integrals). For what values of s is…

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Q: Find the Laplace transform using convolution theorem: Te2" sin(2(t - T))dr.

A: So, here f(t) = sin(2t) and g(t) = t e2t.

Q: Apply the definition of Laplace transform (that is, you have to compute the integral) to find the…

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Q: -4t L {2+ + == ¹²}

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Q: {; .0 2 FİND THE LAPLACE TRANSFORM OF THE FUNCTİON WİTH THE HELP OF THE DEFİNİTİON .(DEFİNİTİON…

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Q: Write down the definition of the laplace transform in terms of an improper integral and use it to…

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Q: Find the laplace transform of f(t) =1/4 e^2t sin(2t)

A: Find the laplace transform of f(t) =1/4 e^2t sin(2t)

Q: Find the Laplace transform of sin 21, 0<t < 2n S(): 0, 12 2n

A: we have given the function f(t) = sin2t,  0≤t≤2π   0,          t≥2π we have to find the Laplace…

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

A: As per the question we are given the definition of Fourier transform of f(t) as F(ω) Amd from that…

Q: kx _f(x) = ek

A: The Fourier integral of a function f(x) is defined as:F(ω)=∫−∞∞f(x)e−iωxdxTo find the Fourier…

Q: Find the Laplace transform of the function f(t) : For this particular problem, use the integral…

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Q: 1 s³ (s-V5)

A: We have to fin the inverse Laplace transform of 1s3s−5 that is L−11s3s−5 First find the partial…

Q: where k > 0. s(s-k)'

A: Using Laplace transform of integrals  L∫0tftdt=1sFs Also,  πss-k=πsFs where Fs=1s-k

Q: Use the definition of Laplace Transform, F(s)=∫∞0e-sx*f(s)dx to show that L{f'(x)}=s*F(s)-f(0).

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