Question

by applying the final-value theorm, find the final value of f(t) whose laplace transform is given by f (s) = 10/s(s 1)

Answer 1

To find the final value of f(t), we apply the final-value theorem to the Laplace transform f(s) = 10/s(s+1), resulting in a final value of 10.

Step-by-step explanation:

The student's question involves applying the final-value theorem to find the final value of a function f(t) given its Laplace transform f(s) = 10/s(s+1). The final-value theorem states that if the limits exist, then limt→∞f(t) = lims→0sF(s), where F(s) is the Laplace transform of f(t). In this situation:

• Multiply the expression by s to apply the theorem: s * (10/s(s+1)) = 10/(s+1).
• Find the limit as s approaches 0: lims→0(10/(s+1)) = lims→0(10/(1+s)).
• Since the limit of 10/(1+s) as s approaches 0 is 10, the final value of f(t) is 10.