Consider f(t) = 3t, g(t) = 4t². Proceed as in this example and find the convolution f g of the given functions. (Write your answer as a function of t.) f*g= After integrating, find the Laplace transform of f* g. (Write your answer as a function of s.) L{fg} =

Q: S ds J V3s? + 1

A: To evaluate the given integral

Q: 64y2+7=32

A: 64y2+7=32

Q: 4y-12=0

A: 4y = 12 y = 3

Q: 1+2x=77

A:

Q: 4w=25

A: topic - linear equation

Q: 3b-12 = 30

A:

Q: -3w+5=23

A:

Q: Using the sketch graphs of y = x' and x+ y=1, show that x' +x-1=0 has only one real root and state…

A: Sketch the graph of polynomial y=x3 and line x+y=1.                         From the graph it can…

Q: {A €R?x2 | tr(A) = 0} | tr(A) — 0}

A: Here we take a general matrix of the given set then find the basis.

Q: -4d = -64

A: Given  -4d=-64

Q: 1+n=15

A: -1+n=15

Q: 8P4 11C7

A:

Q: Find fre dz |2e*dx

A:

Q: -5 -2 1

A:

Q: S V25 – 4x²

A: For the solution follow the next step.

Q: -8 = 6+n

A:

Q: 2: Find: L-1[: 1 3 - 3]

A:

Q: 6+12=

A: Given,          6+12

Q: p dx. -3x (h)

A:

Q: A+12=13

A: Given,   A+12=13     We will solve it for the value of A

Q: 6+197

A: Given,          6+197

Q: Find L s²-8

A:

Q: dx 4е2я — 8ет + 5

A: This question can be solved using the concept of special integrals.

Q: ZV zV1- z?dz

A: Let the given integral be y - y = ∫z1-z2 dz           ..............(1)Let,z = sinx…