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Evaluate $\displaystyle\lim_{x \to \infty} \left(1 + \dfrac{2}{x}\right)^x$.
A$1$
B$e$
C$e^2$
D$2e$
Answer & Solution
Correct answer: C. $e^2$
Apply the standard form $\lim_{x\to\infty}\left(1 + \dfrac{k}{x}\right)^x = e^k$. 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 $1$.
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