Allied & ICAR Exam Bank • ALLIED_2636 NAT • 2 Marks

Section 1: Engineering Mathematics

Calculus

Subtopic: Limit, continuity and differentiability

Question Statement:

The value of $\lim_{x \to \infty} \left(1 + \frac{3}{x}\right)^{2x}$ is $e^k$. The value of $k$ is:

Answer Key:

6

Step-by-Step Solution & Explanation

Standard limit: $\lim_{x \to \infty} \left(1 + \frac{a}{x}\right)^{b x} = e^{a b}$. Here $a = 3, b = 2 \implies e^{3 \times 2} = e^6$. So $k = 6$.
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