A - 500 € est f(t)dt = lim [² e-st f(t). A→∞ Jo cify the domains of the Laplace trans

Q: . Use the definition of Laplace Transformation ( not tables) of L{f (t)} = Je"f(t) L{e $}

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Q: Let y be the curve with vector form r(t) = (1/(t+ 2), sin(sin(sin t)), e-"). a) Determine whether…

A: The parametric curve is r(t)=⟨1t+2, sin( sin( sin t)),e-t⟩. x(t)=1t+2, y(t)=sin( sin( sin t)),…

Q: Find f(t) that corresponds to L[f(t)] transformation. = 1 s² - 4s +8 where L is the Laplace

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Q: Find the Laplace transforms + of (sint + cost).

A: We have to  find the Laplace transformation of -e-t+12sint+cost

Q: Determine whether Laplace's equation in two dimensions a²u a?u + дх2 ду? Is satisfied by the…

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Q: Derive a Dirichlet principle for the elliptic operator L in divergence form with A e C² and b= 0.

A: Given elliptical operator L~ in divergence form with A∈C1 and b=0. Suppose A∈C1Ω of the second order…

Q: Find the domain of vector r(t) and find the limit as t goes to 0 of vector r(t)

A: According to question,Given vector,rt = 2-t, et-1t, lnt+1

Q: L{e2"sin2t + etcos3t}

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Q: Find the Laplace transfomation of the function f(t) : cosh at sinh bt

A: The given function ft=cosh at sinh bt. To find: Laplace transformation of the function. Formula…

Q: f(t) = cos(t 6.

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Q: ƒ(t) = t²,0 < t < 2ñ‚ ƒ(t + 2ñ) = f(t)

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Q: L{e' sinh(t)}

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Q: eot cosat-sinat-1 f(t)

A: Laplace transferom of divisible by t theorem

Q: (c) Let vector Ğ be given by Ğ = (2xz)i + (x²/2)j - (z²)k. Calculate the divergence of G.

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Q: Find the transversality condition for functionals of the form X2 I= [ A(x, y) √ 1 + y^² dx XI when…

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Q: Sketch the bifurcation diagram for the ODE dx dt = rx + x³,

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Q: 0, ts2 2 6

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Q: Use the Laplace transformation to solve the following ODE: y''-y'-12y=2e2t, with y(0)=7, y'(0)=0.…

A: Given: The given ordinary differential equation is y''-y'-12y=2e2t with y(0)=7 ,y'0=0

Q: 3. Find the laplace transforms of f(t) = ¹e²t sin(2t) 2t 4

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Q: Use the two properties L1 and L2 to show that the following are linear transformations. VI (c) T:R³…

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Q: Compute the subdifferential of f(x) = max(1-r,0), for r E Rn.

A: As per the question we have to find the subdiffernetial of the function f(x) = max (1-x,0) And we…

Q: Find the Laplace transforms of f(t) = e(3t-7) cos3(6t).

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Q: (b) Consider the function F : R³→R³ such that 2x1 2x2 cos x3 – e²2r –x3 sin x3 – 2e"2 X3 +4 F(x) =…

A: Definition of Jacobian:        A determinant which is defined for a finite number of functions of…