7. In the process of computing the inverse Laplace transform of the function F(s) = -23 - arctan ¹ (²) an equivalent expression is obtained given by: a s² + 121 What is the value of a?

Q: Ex. Find the Laplace transform for the functions 1-f (t) = sin't %3D 2-f (t) =t°e"

A: We have to use Laplace standard transformations.

Q: Evaluate the triple integral. 3x dV, where E = {(x, y, z) I 0 s y s 2, 0sxs V4- y², 0 s z s 2y}

A: Given region is E=x,y,z/0≤y≤2,0≤x≤4−y2,0≤z≤2y We have to evaluate the triple integral ∭E3xdV in…

Q: y" + 4y' + 4y = 2e, y (0) = 2, y (0) = %3D %3D

A:

Q: 2. F(s): = 3s² +5s-4 S4

A:

Q: 7. Obtain the Fourier sine transform of the following functions: sin wx (c) x² +1' w > 0

A: The given problem is to find the Fourier sine transform of the given function, we have a general…

Q: Find te Inverre laplace transform of F(s) 48 2. |

A: Inverse Laplace Transform Definition: If Fs be the Laplace transform of a function ft, i.e., if…

Q: 6. a) Find the Fouriér Transform of f(x) = 1-x² (x) 1), b) Evaluate, - I Cosx-sinx cosdx

A: We have to solve the given problem using Fourier transform.

Q: 2s3+ 4s²+1 F(s) = (s²+ 2s+17)(s²+ 4s+20)

A:

Q: 2s²+7 F(s) (s+1)(s+2)(s²+ 2s+5)

A:

Q: Find Fourier transform for the following functions:x(t)=3+(sin2wt)2

A: Given function is, xt=3+sin2wt2.      ........1 Fourier transformation: Fourier transformation of…

Q: How is the existence of the Laplace transform of a function guaranteed?

A: We known that the  Existence of the Laplace transform of a function guaranteed

Q: Find sine transform of e-[165]t/t

A: The Fourier sine transform is defined as                                  Fsfx = Fss = ∫0∞fx sinsx…

Q: Find the inverse Fourier transform of the function 10 sin(3) w+T

A:

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

A:

Q: 3. Find the inverse Laplace Transform of the g

A:

Q: 12. Laplace transform is used to convert function in terms of distance into a function in terms of…

A: 12. Laplace transform is used to convert function in terms of distance into        a function in…

Q: 1) Find the Fourier Sine transform of the function f(x) = re %3D

A:

Q: How does one find the inverse Laplace transform for the arccot(1/s)?

A: Let,

Q: (2,0 st 3

A:

Q: The question involves finding the inverse Fourier Transform of the following functions:

A: see the attachment given below for details.Explanation:

Q: Find ℒ{sin(at)}. For what values of s is this transform defined?

A:

Q: Solve the fourier transform of the following functions: 2. f(x) = {x if 0 < x < a otherwise

A:

Q: How do you write the Laplace transform of this translated Heaviside function?

A: Given - ft = 0x &lt; π1x ≥ π To find - Write the Laplace transform of given translated Heaviside…

Q: P(s) = 1 s+ 42 1 (s+ 3)¹

A:

Q: Give the Fourier Transform for the following functions: (i) 108(t)

A: