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How do you find the limit of #(1-(2/x))^x# as x approaches infinity?

1 Answer

Oct 20, 2017

I would rewrite to use #lim_(trarroo)(1+1/t)^t = e# and continuity of the exponential function.

Explanation:

#(1-2/x)^x = (1-1/(x/2))^x = ((1-1/(x/2))^(x/2))^2#

As #xrarr00#, we have #x/2rarroo#, so #((1-1/(x/2))^(x/2))^2rarr e^2#

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