How do you find the limit of #sqrt(x^2 + x + 1) / x# as x approaches infinity? Calculus Limits Determining Limits Algebraically 1 Answer Ratnaker Mehta Aug 25, 2016 Reqd. Limit#=1#. Explanation: Reqd. Limit#=lim_(xrarroo) sqrt(x^2+x+1)/x# #=lim_(xrarroo) sqrt{x^2(1+1/x+1/x^2)}/x# #=lim_(xrarroo) {cancelxsqrt(1+1/x+1/x^2)}/cancelx# #=lim_(xrarroo) sqrt(1+1/x+1/x^2)# #=sqrt(1+0+0)# #=1#. Answer link Related questions How do you find the limit #lim_(x->5)(x^2-6x+5)/(x^2-25)# ? How do you find the limit #lim_(x->3^+)|3-x|/(x^2-2x-3)# ? How do you find the limit #lim_(x->4)(x^3-64)/(x^2-8x+16)# ? How do you find the limit #lim_(x->2)(x^2+x-6)/(x-2)# ? How do you find the limit #lim_(x->-4)(x^2+5x+4)/(x^2+3x-4)# ? How do you find the limit #lim_(t->-3)(t^2-9)/(2t^2+7t+3)# ? How do you find the limit #lim_(h->0)((4+h)^2-16)/h# ? How do you find the limit #lim_(h->0)((2+h)^3-8)/h# ? How do you find the limit #lim_(x->9)(9-x)/(3-sqrt(x))# ? How do you find the limit #lim_(h->0)(sqrt(1+h)-1)/h# ? See all questions in Determining Limits Algebraically Impact of this question 1165 views around the world You can reuse this answer Creative Commons License