How do you evaluate the limit #sqrt(x^2-2)-sqrt(x^2+1)# as x approaches #oo#? Calculus Limits Determining Limits Algebraically 1 Answer Cesareo R. Aug 31, 2016 #0# Explanation: #sqrt(x^2-2)-sqrt(x^2+1) = ((x^2-2)-(x^2+1))/(sqrt(x^2-2)+sqrt(x^2+1))# #=(-3)/(sqrt(x^2-2)+sqrt(x^2+1)) = -(3/x^2)(1/(sqrt(1-2/x^2)+sqrt(1+1/x^2)))# so #lim_(x->oo)sqrt(x^2-2)-sqrt(x^2+1)=-lim_(x->oo)(3/x^2)lim_(x->oo)(1/(sqrt(1-2/x^2)+sqrt(1+1/x^2))) = 0 xx 1/2=0# 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 6099 views around the world You can reuse this answer Creative Commons License