Question Bank • QB_EM_GATE_004 NAT • 2 Marks

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Laplace transforms and their inverse

Question Statement:

The inverse Laplace transform of $F(s) = \frac{s + 7}{s^2 + 6s + 13}$ is evaluated at $t = 0$. The value of $f(0)$ is ________ (in integer).

Answer Key:

1

Step-by-Step Solution & Explanation

By Initial Value Theorem of Laplace Transforms: $f(0) = \lim_{s \to \infty} [s \cdot F(s)] = \lim_{s \to \infty} \left[ \frac{s(s + 7)}{s^2 + 6s + 13} \right] = \lim_{s \to \infty} \frac{s^2 + 7s}{s^2 + 6s + 13} = 1$ Hence, $f(0) = 1$.
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