GATE 2021 IN – Question 53
Given $y(t)=e^{-3t}u(t)*u(t+3)$, where $*$ denotes convolution, $\lim_{t\to\infty}y(t)$ is ______ (two decimal places).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.3 to 0.35
Explanation
y(t)=∫e^(−3τ)u(τ)u(t−τ+3)dτ. For t≥−3 this integrates from 0 to t+3, giving [1−e^(−3(t+3))]/3. As t→∞ the exponential vanishes and the limit is 1/3, rounded **0.33**.