Allied & ICAR Exam Bank • ALLIED_1038 NAT • 1 Mark

Section 1: Engineering Mathematics

Calculus

Subtopic: Indeterminate forms

Question Statement:

The value of $\lim_{x \to 0} (1 + 3x)^{2/x}$ is $e^k$. The value of $k$ is:

Answer Key:

6

Step-by-Step Solution & Explanation

This is of the form $1^\infty$. $\lim_{x \to 0} (1 + 3x)^{2/x} = e^{\lim_{x \to 0} \frac{2}{x} \cdot (3x)} = e^{2 \times 3} = e^6$. Hence $k = 6$.
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