Question

Given \( y(t) = e^{-3t}u(t) u(t + 3) \), where denotes convolution operation. The value of \( y(t) \) as \( t \to \infty \) is \(\underline{\hspace{2cm}}\) (rounded off to two decimal places).
 

Hint:

The convolution of step functions with an exponential decay results in zero as \( t \to \infty \).

Answer 1

Correct Answer: 0.3

The convolution of two unit step functions \( u(t) \) and \( u(t + 3) \) results in a function that is non-zero only for \( t \geq -3 \). As \( t \to \infty \), the exponential term \( e^{-3t} \) tends to 0, thus: \[ y(t) = 0 \, \text{as} \, t \to \infty \] Thus, the value of \( y(t) \) as \( t \to \infty \) is \( 0 \).