What is the limit of f(x) = (2x+5)/abs(3x-4) as x goes to infinity? Calculus Limits Limits at Infinity and Horizontal Asymptotes 1 Answer Sasha P. Oct 18, 2015 2/3 vv -2/3, see the explanation. Explanation: |3x-4|=3x-4 for 3x-4>=0, 3x>=4, x>=4/3 |3x-4|=-3x+4 for 3x-4<0, 3x<4, x<4/3 lim_(x->+oo) (2x+5)/|3x-4| = lim_(x->+oo) (2x+5)/(3x-4) = lim_(x->+oo) (2+5/x)/(3-4/x) = 2/3 lim_(x->-oo) (2x+5)/|3x-4| = lim_(x->-oo) (2x+5)/(-3x+4) = lim_(x->-oo) (2+5/x)/(-3+4/x) = -2/3 Note: 5/x->0 when x->oo vv x->-oo 4/x->0 when x->oo vv x->-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 2514 views around the world You can reuse this answer Creative Commons License