How do you find the limit of #(1/x)^x# as x approaches infinity? Calculus Limits Infinite Limits and Vertical Asymptotes 1 Answer Cesareo R. Jun 2, 2016 #lim_{x->infty}(1/x)^x = 0# Explanation: For #x>1-> 1/x < 1# and considering #a# such that #abs(a) < 1##lim_{x->infty}a^x = 0 # 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 1205 views around the world You can reuse this answer Creative Commons License