Allied & ICAR Exam Bank • ALLIED_0028 MCQ • 1 Mark

Section 1: Engineering Mathematics

Calculus

Subtopic: Taylor and MacLaurin series

Question Statement:

The coefficient of $x^3$ in the Maclaurin series expansion of $\sin(x)$ is:

Options:

  • (A) $-1/6$
  • (B) $1/6$
  • (C) $-1/3$
  • (D) $1$

Answer Key:

A

Step-by-Step Solution & Explanation

Maclaurin series: $\sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \dots = x - \frac{x^3}{6} + \dots$. The coefficient is $-1/6$.
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