How do you find the limit of #f(x) = (x^2 - 1) / ( x + 1) ^2# as x approaches 0? Calculus Limits Determining Limits Algebraically 1 Answer Maharshi · Jim H Feb 27, 2016 #lim f(x) = -1 # as #x -> 0 # Explanation: #f(x) = (x^2-1)/(x+1)^2# #f(x) = ((x+1)(x-1))/((x+1)(x+1)# #f(x) = (x-1)/(x+1)# #So, lim f(x) = (0-1)/(0+1) = -1# as # x # goes to zero. 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 1501 views around the world You can reuse this answer Creative Commons License