1. Let L{f(t)} = | e-f(t)dt be the Laplace transform of the function f(t). Find the Laplace transform of f(t) %3D

e^3(t+2)/2. Find laplace transform of the function

Find the Fourier Cosine Transform of the function if a = 4, b = 9, and c = 6 . Then, evaluate the transform if w = 21

Determine the Fourier transform and plot the magnitude (ii) x(t) = f(x) = (1, \t| < T/2 10, otherwise

f(t) For f(t) = e-t - 1, find the Laplace transform of t Then, for g(t) = e-t – 2, | examine if the Laplace transform of 9(t) exists.

(a) Find the Laplace transform of the functions: f(t) = tsint+e-4²+74³ +44.

a) Express f(t) in terms of unit step functions b) Find the LaPlace transform of f(t)

Find the Laplace transform F(s) = L {f(t)} of the function f(t) = 3e-10t + 9t + 5et, defined for t 0. F(s) = L {3e¬10t + 9t + 5e"} = help (formulas) For what values of s does the Laplace transform exist? help (inequalities)

a) Find the Fourier transform of f(t)=etu(t) + ²+g.

By the definition of Laplace transform find the Laplace transform of the following functions (a) f(() c (b) f(t) = et