How do you find #lim t/sqrt(4t^2+1)# as #t->oo#? Calculus Limits Limits at Infinity and Horizontal Asymptotes 1 Answer James May 20, 2018 #lim_(trarroo)t/sqrt(4t^2+1)=1/2=0.5# Explanation: show below #lim_(trarroo)t/sqrt(4t^2+1)=lim_(trarroo)[(t)/sqrt[t^2(4+1/(t^2))]]# #lim_(trarroo)[(t)/(tsqrt[(4+1/(t^2)))]]==lim_(trarroo)1/sqrt(4+1/(t^2))# #1/sqrt(4+1/(oo))=1/sqrt4=1/2=0.5# Note that #color(red)[c/oo]=0 # where c any constant 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 1715 views around the world You can reuse this answer Creative Commons License