a. Express the function f(t)=- its Laplace transforms. π-t, sin t, 0 π 15 terms of unit step function and hence finc

Q: 4. f (t) = x5e(1-x)

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Q: 5. f(t) = sin (6t).

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Q: a)The graph of the function f(t) The Laplace transform directly implies F(s). Find by definition.…

A: PART A The function graph will be given as follows :

Q: Use the method Laplace transform to solve the following. (a) 2r' + 7r=3e-t, x(0) = 4. (b) 2r' +…

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Q: Q2 \ Determine the Laplace transforms of the following function: t | e-4tt sin? 3t dt L

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Q: sin 3t f(t) t

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Q: Find the Laplace transform of the following: 2. f(t) = v1+ sin t + (5t)18 + t² cos 2t

A: Here given function as ft=1+sin t+5t18+t2cos 2torft=sin2t2+cos2t2+2sin t2cost2+5t18+t2cos…

Q: a) Consider the following function UTM UT Cos t, cos 2t, 0 T. UTM ii. Hence, find its Laplace…

A: The given problem is to express the given function in terms of unit step function and also find the…

Q: Determine the Laplace transforms of 3, 0 12

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Q: solve: y" - Hý + 4y = 4szt; y(0)=2₁ y(a)=5 using Laplace transform

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Q: Find the Laplace transform F(s), given that f(t) is: (a) 2tu(t – 4) (b) 5 cos(t) 8(t – 2)

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Q: Find the linearization of the function a) z = cos(sin y – x); at (-2,0) and use it to approximate…

A: Suppose f(x,y) be a differentiable function at (a,b). Then linearization of f(x,y) at (a,b) is given…

Q: Evaluate using Laplace Transform: 00 2 sin f (t) = dt et

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Q: Write the function in terms of unit step functions. Find the Laplace transform of the given…

A: Laplace transferom of the pice-wise function

Q: 3s Find the Inverse Laplace of s2+4

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Q: infinty use L.23 and L32 of Laplace Transform Table to evaluate Ţ [t] (2t). dt. 0

A: The integralThe Laplace transform of the function f(t)Now, from the Bessel function of the First…

Q: Find the Laplace Transform of the following functions: 1. f(t) = (2e-4t + sin t)²

A: We have to find the Laplace Transform of the following function. 1)  f(t) = (2e-4t+sint)2

Q: Use the Fundamental Theorem of Calculus Part I to find dh/dx given h(x) = cost dt (Hìnt: need…

A: Answer:  By fundamental theorem of calculus  Let fx=∫axbx gt. dt   dfdx=gbx.b'x-gax.a'x

Q: 2) Sketch the graph of the following s functions and find the Laplace transfo a) f1(t) = }4 – t, (o,…

A: Given,      (a)    f1(t)=t0≤t<24-t2≤t<40t≥4      (b)    f2(t)=00≤t<1t1≤t<21t≥2

Q: Apply the translation theorem to find the inverse Laplace transform of the following function. 6s +9…

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Q: Using the derivative theorem, find the Laplace transform of the following functions

A: In this question we need to find a Laplace transform of the given signal.

Q: Using the properties of laplace transform, find [sin t sin h t cos t cosh t)

A: We have to find the Laplace transform.

Q: 3. f (t) = t³

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Q: (d) How many subsets V of A are there so that 1 € V or VOB= Ø? Explain.

A: This question related to set theory . Solution is given below.

Q: Derive the laplace transform for f(t)= 3 e-St

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Q: laplace(u(t-2)sin(t-2) )

A: laplace(u(t-2)sin(t-2) ) = e-2ss2+1

Q: 4.1 Solve by Laplace Transformation U+ + Ux₁ = xt with I.C: u(x₂0) = Sinx ; u(ost) = 0

A: 4. To solve the given partial differential equation (PDE) using Laplace transform, we will follow…