How do you find the limit of #(1-(2/x))^x# as x approaches infinity? Calculus Limits Infinite Limits and Vertical Asymptotes 1 Answer Jim H 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# Answer link Related questions How do you show that a function has a vertical asymptote? What kind of functions have vertical asymptotes? How do you find a vertical asymptote for y = sec(x)? How do you find a vertical asymptote for y = cot(x)? How do you find a vertical asymptote for y = csc(x)? How do you find a vertical asymptote for f(x) = tan(x)? How do you find a vertical asymptote for a rational function? How do you find a vertical asymptote for f(x) = ln(x)? What is a Vertical Asymptote? How do you find the vertical asymptote of a logarithmic function? See all questions in Infinite Limits and Vertical Asymptotes Impact of this question 12235 views around the world You can reuse this answer Creative Commons License