Allied & ICAR Exam Bank • ALLIED_2634 NAT • 2 Marks

Section 1: Engineering Mathematics

Calculus

Subtopic: Limit, continuity and differentiability

Question Statement:

The value of the limit $\lim_{x \to 0} \frac{1 - \cos(4x)}{x^2}$ is:

Answer Key:

8

Step-by-Step Solution & Explanation

Using $1 - \cos \theta \approx \frac{\theta^2}{2}$, here $1 - \cos(4x) = \frac{(4x)^2}{2} = 8x^2$. Thus $\lim_{x \to 0} \frac{8x^2}{x^2} = 8$.
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