How do you find the Limit of #sqrt (x -1) / (sqrt(x+3) - 2) # as x approaches 1? Calculus Limits Determining Limits Algebraically 1 Answer Cesareo R. Jul 31, 2016 #oo# Explanation: Rationalizing the denominator #sqrt (x -1) / (sqrt(x+3) - 2) = (sqrt(x-1)(sqrt(x+3)+2))/(x-1) =(sqrt(x+3)+2)/sqrt(x-1)# then #lim_{x->1}sqrt (x -1) / (sqrt(x+3) - 2) =lim_{x->1}(sqrt(x+3)+2)/sqrt(x-1)=oo# 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 1897 views around the world You can reuse this answer Creative Commons License