#lim_(x->oo)((x-1)/(x+1) )^x =# ? Calculus Limits Determining Limits Algebraically 1 Answer Cesareo R. Feb 18, 2018 #e^-2# Explanation: #(x-1)/(x+1) = (x+1-2)/(x+1) = 1-2/(x+1)# now making #y =- (x+1)/2# we have #lim_(x->oo)((x-1)/(x+1) )^x = lim_(y->oo)(1+1/y)^(-(2y+1))# but #(1+1/y)^(-(2y+1))=1/(1+1/y)(1+1/y)^(-2y)# and then #lim_(x->oo)((x-1)/(x+1) )^x = (lim_(y->oo)1/(1+1/y))(lim_(y->oo)(1+1/y)^(-2y))=e^-2# 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 1110 views around the world You can reuse this answer Creative Commons License