Allied & ICAR Exam Bank • ALLIED_2664 NAT • 2 Marks

Section 1: Engineering Mathematics

Calculus

Subtopic: Fourier, Taylor and MacLaurin series

Question Statement:

In the Taylor series expansion of $f(x) = \ln(1 + x)$ about $x = 0$, the coefficient of $x^3$ is $\frac{1}{k}$. The value of $k$ is:

Answer Key:

3

Step-by-Step Solution & Explanation

$\ln(1 + x) = x - \frac{x^2}{2} + \frac{x^3}{3} - \dots$ The coefficient of $x^3$ is $1/3$, so $k = 3$. (Taking absolute value/denominator $k=3$).
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