Allied & ICAR Exam Bank • ALLIED_2668 NAT • 1 Mark

Section 1: Engineering Mathematics

Calculus

Subtopic: Fourier, Taylor and MacLaurin series

Question Statement:

The Maclaurin series expansion of $e^{-x^2}$ up to the quadratic term is $1 - k x^2$. The value of $k$ is:

Answer Key:

1

Step-by-Step Solution & Explanation

Substituting $u = -x^2$ into $e^u = 1 + u + \dots$ gives $1 - x^2 + \dots$ so $k = 1$.
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