What is the limit of # (x^3 - 2x +3) / (5-2x^2)# as x goes to infinity? Calculus Limits Limits at Infinity and Horizontal Asymptotes 1 Answer Jim H Oct 23, 2015 #lim_(xrarroo) (x^3 - 2x +3) / (5-2x^2) = -oo# Explanation: #lim_(xrarroo) (x^3 - 2x +3) / (5-2x^2)# has indeterminate form #oo/oo#. For all #x !=0# we get #(x^3 - 2x +3) / (5-2x^2)= (x^2(x-2/x+3/x^2))/(x^2(5/x^2-2))# So #lim_(xrarroo) (x^3 - 2x +3) / (5-2x^2) =lim_(xrarroo) (x-2/x+3/x^2)/(5/x^2-2) =oo/-2 = -oo# Answer link Related questions What kind of functions have horizontal asymptotes? How do you find horizontal asymptotes for #f(x) = arctan(x)# ? How do you find the horizontal asymptote of a curve? How do you find the horizontal asymptote of the graph of #y=(-2x^6+5x+8)/(8x^6+6x+5)# ? How do you find the horizontal asymptote of the graph of #y=(-4x^6+6x+3)/(8x^6+9x+3)# ? How do you find the horizontal asymptote of the graph of y=3x^6-7x+10/8x^5+9x+10? How do you find the horizontal asymptote of the graph of #y=6x^2# ? How can i find horizontal asymptote? How do you find horizontal asymptotes using limits? What are all horizontal asymptotes of the graph #y=(5+2^x)/(1-2^x)# ? See all questions in Limits at Infinity and Horizontal Asymptotes Impact of this question 9844 views around the world You can reuse this answer Creative Commons License