Question

3A Solve and verify the initial and final value theorem for: $f(t) = e^{-t}(t+1)^2$ 3B Analyse the Laplace transform: $f(t) = [A + Be^{-bt}]u(t)$ 3C Interpret the inverse Laplace transform: $\frac{(3s + 1)}{(s + 1)(s^2 + 2)}$

          3A Solve and verify the initial and final value theorem for:
$f(t) = e^{-t}(t+1)^2$
3B Analyse the Laplace transform:
$f(t) = [A + Be^{-bt}]u(t)$
3C Interpret the inverse Laplace transform:
$\frac{(3s + 1)}{(s + 1)(s^2 + 2)}$

Added by Danielle G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

06/28/2023

Step 1

The initial value theorem states that lim(s->∞) sF(s) = f(0), and the final value theorem states that lim(t->∞) f(t) = lim(s->0) sF(s). First, we need to find the Laplace transform F(s) of ft=e^-t+t+1. The Laplace transform of e^-t is 1/(s+1), the Laplace Show more…

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Answer the following 3A Solve and verify the initial and final value theorem for ft=e-+t+1 Analyse the Laplace transform: ft=[A+Be-bt]ut Interpret the inverse Laplace transform: 3s+1 s+1s+2 3B 3C