Discussion
The value of \( \lim_{x \to \infty} \left(1 + \dfrac{3}{x}\right)^{2x} \) is
Answer: C
Take logarithms and let \( L \) be the limit:
\[ \ln L \;=\; \lim_{x \to \infty} 2x \ln\!\left(1+\frac{3}{x}\right) \;=\; \lim_{x \to \infty} 2x \cdot \frac{3}{x} \;=\; 6, \]
using \( \ln(1+t) \approx t \) for small \( t \). Hence \( L = e^{6} \). The general rule is that \( (1+a/x)^{bx} \to e^{ab} \), and here \( ab = 3 \times 2 \)
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