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GATE 2021 ME (ME2) – Question 12

Engineering Mathematics · Differential Equations: Initial and boundary value problems, Laplace transforms · 1 mark · Multiple choice

If the Laplace transform of a function $f(t)$ is given by $\mathcal L\{f(t)\}=\frac{s+3}{(s+1)(s+2)}$, then $f(0)$ is

  1. 0
  2. $1/2$
  3. 1
  4. $3/2$

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Show answer and explanation

Correct answer: (C) 1

Explanation

The initial-value theorem gives $f(0^+)=\lim_{s\to\infty}sF(s)$. Here numerator and denominator have equal leading coefficient after multiplication by s.

Thus the limit is **1 (C)**. Direct inversion, f=2 e⁻ᵗ−e⁻²ᵗ, confirms f(0)=1.