How do you determine the limit of #(3/x^3) ((x-2)/(x-1))# as x approaches 1-? Calculus Limits Determining Limits Algebraically 1 Answer Jim S May 19, 2018 #lim_(xrarr1^(-))3/x^3*((x-2)/(x-1))=-oo# Explanation: #lim_(xrarr1^(-))(3(x-2))/(x^3(x-1))=# #lim_(xrarr1^(-))3/x^3*((x-2)/(x-1))=-oo# because #x->1^-# #<=># #x-1<0# so #lim_(xrarr1^(-))1/(x-1)=^((1/0^(-)))=-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 1361 views around the world You can reuse this answer Creative Commons License