How do you find the limit of #sqrt(x)*(sqrt(x+8) - sqrt(x-6))# as x approaches #oo#? Calculus Limits Determining Limits Algebraically 1 Answer Cesareo R. Oct 24, 2016 #7# Explanation: #sqrt(x)*(sqrt(x+8) - sqrt(x-6))(sqrt(x+8) +sqrt(x-6))/(sqrt(x+8) + sqrt(x-6)) =# #=sqrt(x)(x+8-(x-6))/(sqrt(x+8) + sqrt(x-6)) =(14sqrt(x))/(sqrt(x+8) + sqrt(x-6))= # #=sqrt(x)/sqrt(x)14/(sqrt(1+8/x)+sqrt(1-6/x)) = 14/(sqrt(1+8/x)+sqrt(1-6/x))# then #lim_(x->oo)sqrt(x)*(sqrt(x+8) - sqrt(x-6))=lim_(x->oo)14/(sqrt(1+8/x)+sqrt(1-6/x))=7# 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 2213 views around the world You can reuse this answer Creative Commons License