What is the limit of #(sin^4x)/(x^(1/2))# as x approaches infinity? Calculus Limits Limits at Infinity and Horizontal Asymptotes 1 Answer Alan P. Apr 19, 2016 #lim_(xrarroo)(sin^4 x)/(x^(1/2)) = 0# Explanation: #sin x# is limited to the range #[-1,+1]# #rarr sin^4 x# is limited to the range #[0,1]# #rarr sin^4 x# has an upper limit of #1# while #xrarroo# #x^(1/2) rarr oo# as #xrarroo# 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 2178 views around the world You can reuse this answer Creative Commons License