Question

Apply Theorem 2 to find the inverse Laplace transforms of the functions in Problems 17 through 24.

F(s) = 1/s(s-3)

Answer 1

To find the inverse Laplace transform of the function F(s) = 1/s(s-3), we can use Theorem 2 by factorizing the denominator into partial fractions.

Step-by-step explanation:

To find the inverse Laplace transform of the function F(s) = 1/s(s-3), we can use Theorem 2. According to Theorem 2, if F(s) is a rational function with distinct linear factors in the denominator, then its inverse Laplace transform is given by the sum of partial fraction terms.

First, we need to factorize the denominator to partial fractions: 1/s(s-3) = A/s + B/(s-3). To find the values of A and B, we can manipulate this algebraically. We get A(s-3) + Bs = 1. By substituting known values (s=0 and s=3), we can solve for A and B. Once we have A and B, we can take the inverse Laplace transform of each partial fraction term and add them together to get the final answer.