Determine the Laplace Transform of the functionf(t)=7u1(t)

The Laplace Transform of a function f(t) is given by the integral from 0 to infinity of e^(-st)f(t) dt.

The function given is f(t) = 7u1(t), where u1(t) is the unit step function. The unit step function is 0 for t < 1 and 1 for t >= 1.

So, the Laplace Transform of f(t) is the integral from 1 to infinity of 7e^(-st) dt.

This is a simple exponential integral, and can be solved as follows:

L{f(t)} = ∫ from 1 to ∞ [7e^(-st) dt] = [-7/s * e^(-st)] from 1 to ∞

Evaluating this from 1 to infinity gives:

= 0 - (-7/s * e^(-s)) = 7e^(-s)/s

So, the Laplace Transform of the function f(t) = 7u1(t) is 7e^(-s)/s.