Question #4e666 Calculus Limits Infinite Limits and Vertical Asymptotes 1 Answer Eddie Apr 25, 2017 #L = lim _(x->oo) (1/x)^lnx# #ln L = lim _(x->oo) ln x cdot ln (1/x)# #= lim _(x->oo) ln x cdot (ln 1 - ln x))# #implies ln L = lim _(x->oo) - ln^2 x# #implies L = lim _(x->oo) 1/e^( ln^2 x) # # = 1/e^(lim _(x->oo) ln^2 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 1524 views around the world You can reuse this answer Creative Commons License