Aspire Faculty ID #12123 · Topic: CUET 2025 · Just now
CUET 2025

The value of $\lim_{x\rightarrow\infty}(1+\frac{2}{3x})^{x}$ is:

Solution

We use the standard result: \[ \lim_{n \to \infty} \left(1 + \frac{k}{n}\right)^n = e^k \] Here, \(k = \tfrac{2}{3}\) and \(n = x\). \[ \therefore \;\; \lim_{x \to \infty} \left(1 + \frac{2}{3x}\right)^x = e^{\tfrac{2}{3}} \] Final Answer: \( e^{\tfrac{2}{3}} \)

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