Allied & ICAR Exam Bank • ALLIED_0778 NAT • 2 Marks

Section 1: Engineering Mathematics

Calculus

Subtopic: Taylor series

Question Statement:

In the Taylor series expansion of $f(x) = e^{2x}$ about $x = 0$, the coefficient of $x^3$ is $\frac{2^3}{3!} = \frac{8}{6}$. In decimal form (rounded off to two decimal places), this is:

Answer Key:

1.33

Step-by-Step Solution & Explanation

Coefficient is $\frac{f'''(0)}{3!} = \frac{8 e^0}{6} = \frac{8}{6} = 1.3333 \approx 1.33$.
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