How do you find the limit of #((e^x)-x)^(2/x)# as x approaches infinity? Calculus Limits Infinite Limits and Vertical Asymptotes 1 Answer Cesareo R. Aug 18, 2016 #e^2# Explanation: #(e^x-x)^(2/x) = (e^x(1-x/e^x))^{2/x} = e^2(1-x/e^x)^{2/x}# but #lim_{x->oo}(1-x/e^x)^{2/x}=1# so #lim_{x->oo}(e^x-x)^(2/x)=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 5517 views around the world You can reuse this answer Creative Commons License