Evaluate $\displaystyle\lim_{x o \infty} \left(1 + \dfrac{2}{x} igh…

Question

Evaluate $\displaystyle\lim_{x 	o \infty} \left(1 + \dfrac{2}{x}ight)^x$.

Accepted Answer

C. $e^2$

Apply the standard form $\lim_{x	o\infty}\left(1 + \dfrac{k}{x}ight)^x = e^k$. With $k = 2$, the limit is $e^2$.
Option D ($1$) treats this as $1^{\infty} = 1$, which is incorrect — $1^{\infty}$ is an indeterminate form, not equal to $1$.

Answer

$1$

Answer

$e$

Answer

$2e$

Evaluate $\displaystyle\lim_{x \to \infty} \left(1 + \dfrac{2}{x}\right)^x$.