laplace transform of 5t^4e^(-7t)?

Answer 1

f(t) = 5 * t^4 * exp(-7*t) is of the form:

f(x) = x^n * exp(-a*x)

Functions of this form, with n = an integer > 0 have Laplace transforms equal to:

L[f(x)] (s) = n!/((s + a)^(n+1))

For your function, n = 4 and a = 7, so:

L[f(t)] (s) = 5 * 4!/(s+7)^5 = 120/(s+7)^5

See source for a table of transforms.

Answer 2

I think it's 5 * 4! / ((s+7)^5), but don't quote me on it. I forgot all the properties of Laplace transforms. You should be able to find a table online or in a textbook, though.

Answer 3

just search for the table and you can solve it.