1. Find the Laplace transform of the following: a) f(x) = x5 e-* b) f(x) = x3 + 3 cos2x 2. Find the inverse Laplace transforms, as a function of x , of the following functions: 1 a) 2s-3 2s+1 b) (s-1)2+7 2 c) (s2 +1) (s-1)2

Q: Let Rt) be the inverse Laplace transform of 7s2 + 15s – 6 F(s) = (s? + 6s + 10)(s – 2) What is 3/2)?

A:

Q: Show that d(w) - = [6(w− 1) + 6(w+1)] is the Fourier transform of cos(t). Show that d(w) = −ix[8(w −…

A:

Q: 2. (a) Show that gi(t)g2(t) G₁(f) * G₂(f) where denotes convolution and gi(t) = G₁(f), 92(t)=G₂(f).…

A: We start with the time-domain signals and their Fourier transforms:Now, the convolution in the time…

Q: 2. Calculate the inverse Laplace transform: 2s (a) C- C-¹ { 25+32 }; (b) C-¹ ( 25-3₂} 2s L-1

A: We have to find the Laplace inverse transformation of and

Q: Q1. Find the Fourier of the function in Fig.Q1 f(x) -a a x -a Fig.Q1

A: Q1.The function in Fig.Q1 is a sawtooth wave. The function can be defined as:f(x)=πa​xFourier Series…

Q: XP+2ap +2a') ple 23: Find the inverse Fourier sine transform f(x) of F, (P- ap

A:

Q: Find the Fourier Transforms of the indicated function: f (x) = xe-|x|

A:

Q: the Inverse Fourier Transform x(t) of each signal X(w) given below. X(w) = -4 sinc² X(w) = πd(w − 1)…

A: "Since you have posted multiple questions, we will provide the solution only to the specified sub…