How do you find the limit #lima^x# as #x->oo#? Calculus Limits Infinite Limits and Vertical Asymptotes 1 Answer Jim H Dec 31, 2016 Use #a^x = e^(xlna)# and consider cases. Explanation: For #0 < a < 1#, we have #lna < 0#, so as #xrarroo#, we get #xlnararr-oo# and so #a^x rarr 0#. For #a=0#, we get the indeterminate form #1^oo#. For #a > 1#, we have #lna > 0#, so as #xrarroo#, we get #xlnararroo# and so #a^x rarr oo#. 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 1402 views around the world You can reuse this answer Creative Commons License