lim x → ∞ ( 1 + x 2 ) x =, e, e 1 , e 2, None of these

[ lim x → ∞ ( 1 + x /2 1 ) x /2 ] 2 = e 2 as $\lim _{x \rightarrow \infty}\left(1+\frac{1}{x}\right)^x=e$

lim x → ∞ ( 1 + x 2 ) x =

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$\lim _{x \rightarrow \infty}\left(1+\frac{2}{x}\right)^x=$

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Options:

A $e$
B $\frac{1}{e}$
C $e^2$
D None of these

Solution:

2393 Upvotes Verified Answer

The correct answer is: $e^2$

$\left[\lim _{x \rightarrow \infty}\left(1+\frac{1}{x / 2}\right)^{x / 2}\right]^2=e^2$ as $\lim _{x \rightarrow \infty}\left(1+\frac{1}{x}\right)^x=e$

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