Question Bank • QB_SUB_EM_0148 MCQ • 1 Mark

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Laplace transforms and their inverse

Question Statement:

The Laplace transform of $f(t) = e^{4t}$ for $s > 4$ is:

Options:

  • (A) $\frac{1}{s - 4}$
  • (B) $\frac{1}{s + 4}$
  • (C) $\frac{4}{s^2 + 4^2}$
  • (D) $\frac{s}{s^2 - 4^2}$

Answer Key:

A

Step-by-Step Solution & Explanation

$\mathcal{L}\{e^{at}\} = \int_0^\infty e^{-st} e^{at}\, dt = \int_0^\infty e^{-(s-a)t}\, dt = \frac{1}{s - a}$ Here $a = 4$, so $\mathcal{L}\{e^{4t}\} = \frac{1}{s - 4}$.
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