How do you find #lim sqrt(x+2)/(sqrt(3x+1)# as #x->oo#? Calculus Limits Limits at Infinity and Horizontal Asymptotes 1 Answer Eddie Mar 2, 2017 # = 1/sqrt(3)# Explanation: #lim_(x to oo) lim sqrt(x+2)/(sqrt(3x+1)# #= lim_(x to oo) lim (sqrt(x) (sqrt(1+2/(sqrt x))))/(sqrt x (sqrt(3+1/(sqrt x)))# #= lim_(x to oo) lim ( (sqrt(1+2/(sqrt x))))/( (sqrt(3+1/(sqrt x)))# # = 1/sqrt(3)# 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 1663 views around the world You can reuse this answer Creative Commons License