Functions Question 692

Question: $ \underset{x\to \infty }{\mathop{\lim }},{{( 1+\frac{2}{x} )}^{x}}= $

Options:

A) e

B) $ \frac{1}{e} $

C) $ e^{2} $

D) None of these

Show Answer

Answer:

Correct Answer: C

Solution:

$ {{[ \underset{x\to \infty }{\mathop{\lim }},{{( 1+\frac{1}{x/2} )}^{x/2}} ]}^{2}}=e^{2}. $