Allied & ICAR Exam Bank • ALLIED_0040 NAT • 2 Marks

Section 1: Engineering Mathematics

Calculus

Subtopic: Limit, continuity and differentiability

Question Statement:

The value of $\lim_{x \to \infty} \left( 1 + \frac{2}{x} \right)^x$ is equal to $e^k$. The value of $k$ is:

Answer Key:

2

Step-by-Step Solution & Explanation

Standard limit: $\lim_{x \to \infty} (1 + a/x)^x = e^a$. Here $a = 2$, so limit is $e^2$, hence $k = 2$.
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