Allied & ICAR Exam Bank • ALLIED_2633 MCQ • 1 Mark

Section 1: Engineering Mathematics

Calculus

Subtopic: Limit, continuity and differentiability

Question Statement:

The value of $\lim_{x \to 0} \frac{\sin(3x)}{\tan(5x)}$ is:

Options:

  • (A) $3/5$
  • (B) $5/3$
  • (C) $1$
  • (D) $0$

Answer Key:

A

Step-by-Step Solution & Explanation

Using standard limits: $\lim_{x \to 0} \frac{\sin(3x)}{3x} \frac{5x}{\tan(5x)} \frac{3}{5} = 1 \times 1 \times \frac{3}{5} = \frac{3}{5}$.
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