Q4 Solve step Functions in Laplace transform t < 6 x ≥ 0 f(t)= = { = 8+ (-8+ (t-6)²

Q: = Find the inverse Laplace transform f(t) = L-¹ {F(s)} of the function F(s) = f(t)= [38+4 +36 = L-1,…

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Q: (a) For n20 write out the first four terms of the sequence a(n) =(-3)" and then use the definition…

A: Given that, xn=-3n

Q: -* is -. р Show that the finite sine transform of 1 . TC

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Q: 5s + 20 F(s) = s2 + 8s + 97

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Q: Consider the function f(x) = x + 2 sin(x) for - <x<. Find (f-1)'c0). (5-1)'(M) = help (numbers)

A: Note that for x=0, f(x)=0 Then we will find f'(0)

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: Look for the inverse Laplace transform L^ -1 {s-2/(s^2+2s+26}

A: Given expression is L−1s−2s2+2s+26 We have to find the inverse Laplace transform. First of all, we…

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

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Q: If * represents convolution, determine the Laplace transform of f(t) = 12t * e-3t

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Q: The Fourier Cosine transform of the function f(X) = {1, |x| a} a A 1/(/2n)*(cos(as)/s) B…

A: Given functionfx=1,x&lt;a0,x&lt;aFourier cosine transform of f(x) is given byFcfx2=2π ∫0∞ f(x)…

Q: Determine The Fourier transform of the following function (2 |t| t/2 f(t) =

A: Fourier transformation of the function f(t): Fourier transformation of the function f(t) is given…

Q: By using convolution theorem for Laplace transform, prove that 1 L-1 + x}={erf (2√x) PVp +4

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Q: Find f[g(x)] and g[f(x)] for the given functions. 3 f(x) = -x³ -x+2, g(x) = 3x + 5 f[g(x)] =…

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Q: Q3\ Find the Laplace Transform to the following function L sin2t cos3t

A: Using Laplace transform

Q: Find the inverse Laplace transform L-1{F(s)} of the function 6 F(s) = (s – 1) NOTE: The answer…

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Q: Evaluate L{t sin kt} (Use the Derivatives of Transform)

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Q: From the definition, derive a general expression for the form of the DTFT of functions of the form…

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Q: Use formulas from this course to find the inverse Laplace transform (a) L-1{+1) 2s+1 1 252+8 (b)…

A: Solution:

Q: List all intervals for which there are possible unique solutions (t-5)x''-ln(t)y'-y=et

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Q: Consider the function f(x) = (4 - 5x)7. Find the second derivative f"

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Q: Determine the domain and range of function f(x) = elnñ — arcsin (1²²)

A: This question can be solved using the concept of domain and range of inverse trigonometric…

Q: Q3\Find the Laplace transform of f(t) defined as 03

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