What is the limit of ${(1 + \frac{1}{x})}^{x}$ $(1+1/x)^x$ as x approaches infinity?

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Answer 1 · 2017-05-28T09:20:33

$lim_"x->oo" (1+1/x)^x=e approx 2.71828$

Consider the standard limit: $lim_"x->oo" (1+k/x)^x = e^k$

In the example $k=1$

Hence, $lim_"x->oo" (1+1/x)^x = e^1$

$=e approx 2.71828$

What is the limit of (1+1/x)^x(1+1x)x(1+1/x)^x as x approaches infinity?