How do you find the limit #lim x^-x# as #x->oo#? Calculus Limits Infinite Limits and Vertical Asymptotes 1 Answer Eddie Jan 1, 2017 #= 0# Explanation: #lim_(x to oo) x^(-x) # #= lim_(x to oo) exp(ln x^(-x) )# #= lim_(x to oo) exp(- xln x )# #= lim_(x to oo) exp( - lim_(x to oo) x * lim_(x to oo) ln 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 1308 views around the world You can reuse this answer Creative Commons License