Question Bank • QB_EXP_EM_LIM_004 MCQ • 1 Mark

Section 1: Engineering Mathematics

Calculus: Limits, Continuity & Differentiability

Subtopic: L'Hospital's rule

Question Statement:

The value of the limit $\lim_{x \to 0} \frac{\sin(5x)}{x}$ is equal to:

Options:

  • (A) 5
  • (B) 1
  • (C) 0
  • (D) \infty

Answer Key:

A

Step-by-Step Solution & Explanation

Applying the standard limit identity or L'Hospital's rule (0/0 form): $\lim_{x \to 0} \frac{\sin(5x)}{x} = \lim_{x \to 0} \frac{5 \cos(5x)}{1} = 5 \cos(0) = 5$ Hence, the limit value is $5$.
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