(a) Let F(s) be the Luplace transform of f(t). Find the Luplace Transform for [[f (u)+ 2sin(3u)]du. (b) Using Laplace Transform to solve the second order differential equation for x(t). d'x +9x = f(t), (t if 0st<1, R iflst, dr where f(t) =- dx x(0) = 0, (0) = 0, %3D dt

Q: y''+y'=0 where y(0)=0, y'(0)=1 laplace transform of derivatives

A: Given that:-  y" + y' = 0 and y(0)= 0, y'(0) =1 We find laplace transform of this differential…

Q: 7. Evaluate y" + y' = t; y(0) = 1 , y'(0) = -2

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Q: 2. Let F(x) = x s sin (t2) dt. Find F'(x). (a) sin (x²) dx (b) sin (x²) (c) sin (x²) + C (d) 2x sin…

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Q: 4] Find the Laplace Transform of f(t) = { S-1 (-/= + 5 = /₁1) (1te - 1/₁1) (a) (c) S S - I (b) (d) S…

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Q: Find the Laplace transform F(s) = L {f(t)} of the function f(t) = (3 – t) (u₂(t) — u₁(t)) F(s) = L…

A: Formula of Laplace transform  Lu(t-c)=e-cssLtkf(t)=(-1)kdkdsk(F(s))

Q: Find the cosine transform fe(w) of f(x) for f (x) = -6 if 0 2. f.(w) %3D

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Q: y" + y' = t; y(0) = 1 , y'(0) = -2

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Q: 1. (a) Construct the first Taylor approximant to f: (−1,1) → R, ƒ(x) = sin¯¹ x about a = 11. (b) Use…

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Q: Use differentiation in time domain to solve the the Laplace transform: y"-y'-6y=0; y(0)=6, y'(0)=13

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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: Consider the following. F(x) = dt (a) Integrate to find F as a function of x. F(x) = (b) Demonstrate…

A: Second fundamental theorem : Suppose f is continuous function in an open interval I .Let a∈I and a…

Q: 1.a Find the Laplace transform of the function F(t) = e-2t (cosh 3t + sinh 5t)

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Q: Let f(x, y) = x² + y² and r(t) = (cos 1, sin t). (a) Find f(r(1)) without making any calculations.…

A: a) Equation of the circle with the centre at the origin that is (0,0) is x2+y2=a2 then every point…

Q: Use differentiation in time domain to solve the the Laplace transform: y"+7y'+12y=21e³t; y(0)=7/2,…

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Q: 2. ts) Use the table of Laplace Transforms and 1st shifting theorem to find the Laplace transform of…

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Q: Part A how that L(tnf(t)) = (−1)n ((dnF(s))/(dsn)), where F(s) is the laplace transform of y(t). In…

A: Hi, It is multiple sub-parts, I am going to solve the first part only.

Q: 5 The inverse Laplace transform of F(s) = 5² - 2s+5 1 f(t) = 5e²¹ sin 2t f(t) = 5e¹ sin 2t 5 f(t) =…

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Q: What is the Fourier transform of 8(x) dx F(k) = 100 = 2T -ikx 8(x) =?

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the Laplace transform of the given function; a and b are real constants. f(t) = e** sinh(bt)…

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Q: Find a function f(x) whose Laplace transform is e-3p p² +25 You should find f(x) = K sin(R(x -…

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Q: ) Use L(x) to approximate f(16.1).

A: For a given function f(x) the linearization at a point x=a is denoted by L(x) and it is defined as…

Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a = 3 L(x)

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Q: Approximate f' (1) using the given data f(0) = 1, f(1) = 2, f(2) = 1, and f(3) = 10 and the Lagrange…

A: Lagrange inteerpolation is used to find a polynomial equation which passes through the given set of…

Q: 3. Let f(x)= :/ arcsin(t) dt and g(x)= / arccos(t) dt. 0. 0. I f'(x) g' (x) dx =? 4 - T (a) 2 - T…

A: Given Applying derivative with respect to x: Similarly:

Q: Calculate the derivative of the function r(t) i+ cos' (61)j + lIn (2t³)k. t - 2

A: Given : r(t)=-5t-2 i +cos-1(6t)  j +ln2t5 k We have to calculate the derivative of the given…