Allied & ICAR Exam Bank • ALLIED_2718 NAT • 2 Marks

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Laplace transforms and their inverse

Question Statement:

By the Initial Value Theorem, for $F(s) = \frac{2s + 5}{s^2 + 3s + 2}$, $\lim_{t \to 0^+} f(t) = \lim_{s \to \infty} s F(s)$ equals:

Answer Key:

2

Step-by-Step Solution & Explanation

$\lim_{s \to \infty} s \frac{2s + 5}{s^2 + 3s + 2} = \lim_{s \to \infty} \frac{2s^2 + 5s}{s^2 + 3s + 2} = 2$.
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