the Laplace Transforms of the following (t) = 3. You must answer this part by integration, not using tables. t) = (t + cos t)² (you may use tables).

Q: 00 1. Find the laplace transform of, f(t) =sin(t +a)cos(t -a) using e-stf(t)dt.

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Q: Find the Laplace transform of the following: 1. f(t) = e-2t+5) sin³(8t) 3

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Q: Y = f+₁ + fot-, h= 71

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Q: Using the tables write down the transforms of the following functions/ (i) t² – 3t + 4 (ii) 2 cost…

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Q: 2 sin (t) cos (t)d J

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Q: Q: The Fourier representation of a function f(x): f(x) = {-10 V, 10 V, ーTくX x > 0 40 sinx sin3x…

A: Given f(x) = -10v.  When -π < x < 0              = 10v when 0 < x < π.   Graph of this…

Q: i). ƒ (1) = (5– 312) ² i). ƒ (1) =r2sinh (21) Find the Laplace transforms of the following…

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Q: A function f(t) is given as f(t) = e' cos 2t cos t %3! Find the Laplace transform of this function.

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Q: (i) Find L(cos(at + b)] where a and b are constants. (ii) Using Laplace transform, evaluate fote-³t…

A: Disclaimer:  Since you have asked multiple question, we will solve the first question for you. If…

Q: Solve equation using Laplace transform ÿ + 9y = 8 (t -) |sin(t), y(0) = 0, ý(0) = 0

A: Formulae:  1. Lf(t)δ(t-a)=e-asf(a) 2. Lf''(t)=s2F(s) - sf(0)-f'(0) 3. L-1e-asF(s)=H(t-a)f(t-a),…

Q: sin 3at where a is any positive constant and s > a. WHAT IS THE LAPLACE TRANSFORM OF THIS?

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Q: i). ƒ (t) = ²) ² ii). ƒ (t) =t²sinh (21) (5–31

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

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Q: 25. Find the general solution of the equation dy = 2y + 2e-. dt (This equation is linear, but please…

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Q: )L{sinh(7t) + (2t + 1)U (t – 1)},

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Q: ii) using the Fourier Transforms, Calculate dx. Jo (4x*)(9+x*)'

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Q: Rectangle PQRS is reflected across the x-axis. The image is P'Q'R'S'.Which two further…

A: Given Rectangle PQRS is reflected across x axis then image is P'Q'R'S'

Q: 2. Y(s) = J(2s – 3)5 %3D

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Q: (9) 3 ov 1-1) dx

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Q: Find the Laplace transform of the following: 1. 4t + 12 2. 1.5 sin(3t-3)

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Q: 15. Solve the IVP using Laplace transforms. x'(t) = t?, x(0) = 4

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Q: 1. Find the equation of a line perpendicular to y = 1 through A(-1, 1).

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Q: Find the Laplace transform of f(t), where ƒ(t) is f(t)=4e³ sint cost and f(t)=r’sinh2t .

A: We know that  Leat sin(bt) = b(s-a)2+b2. Now  Lf(t)=L4 e3t sint cost= 2 L e3t 2sint cost= 2 L{e3t…

Q: How to solve the Laplace transform of the following equation: W(t)=cos(3t) - cos(7t) Please write…

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Q: Vx2-1 dx

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Q: Calculate the derivative d da 34 dt using Part 2 of the Fundamental Theorem of Calculus. 34 d dx…

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Q: Consider the functions h : R→R and g : R -R defined by h(x) = 72 (5 + arctan(sinh 4æ)), . g(x) = 144…

A: Using inverse trigonometric  function properties

Q: 1° cos(3r) dr COS

A: Given, ∫x2cos3xdx  We have to evaluate the integral.

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…

Q: Let f(x) = e cosx, sx %3D 2. Express your answers in exact form. ElN

A: Inflection point occurs when the second derivative of the function equals to zero.