Question

For x $\in$ R, $lim_{ x \to \infty} \bigg( \frac{x - 3}{ x + 2}\bigg)^x$ is equal to

• A. e
• B. $e^{-1}$
• C. $e^{-5}$
• D. $e^5$

Answer 1

Answer: (D)

$e^5$

Answer 2

For x $\in$ R, $lim_{ x \to \infty} \bigg( \frac{x - 3}{ x + 2}\bigg)^x = lim_{x \to \infty} \frac{(1 - 3 / x)^x }{ (1 + 2 / x)} = \frac{e^{-3}}{e^2} = e^{-5}$