How do you evaluate the limit #x/(sqrt(3x^2+1)# as x approaches #oo#? Calculus Limits Determining Limits Algebraically 1 Answer Alan N. · mason m Jun 19, 2017 #1/sqrt3# Explanation: Let #L = lim_(x->oo) x/(sqrt(3x^2+1))# #= lim_(x->oo) (x/x)/(1/x(sqrt(3x^2+1)))# #= lim_(x->oo) 1/sqrt((1/x^2(3x^2+1)))# #= lim_(x->oo) 1/sqrt((3 + 1/x^2))# #= 1/(sqrt(3+0)) = 1/sqrt3# 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 2675 views around the world You can reuse this answer Creative Commons License