Allied & ICAR Exam Bank • ALLIED_0024 NAT • 2 Marks

Section 1: Engineering Mathematics

Calculus

Subtopic: Limit, continuity and differentiability

Question Statement:

The limit $\lim_{x \to 0} \frac{e^{3x} - 1 - 3x}{x^2}$ is equal to:

Answer Key:

4.5

Step-by-Step Solution & Explanation

Expanding $e^{3x} = 1 + 3x + \frac{(3x)^2}{2!} + \dots \implies \frac{9x^2 / 2}{x^2} = 4.5$.
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