How do you find the limit of #((1/(x+3))-(1/3))/x# as x approaches 0? Calculus Limits Determining Limits Algebraically 1 Answer Ultrilliam Aug 7, 2018 # ((1/(x+3))-(1/3))/x |_(x to 0)# #= ( (3 - (x+3))/(3(x+3))) /x |_(x to 0)# #= -( ( x )/(3(x+3))) /x |_(x to 0)# #= - ( x )/(3x(x+3)) |_(x to 0) # #= - ( 1 )/(3 (x+3)) |_(x to 0) # #= - 1/9# 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 18330 views around the world You can reuse this answer Creative Commons License