How do you find the Limit of #(sin^3 x )/ (sin x - tan x)# as x approaches 0? Calculus Limits Determining Limits Algebraically 1 Answer Cesareo R. Jul 22, 2016 #-2# Explanation: #(sin^3 x )/ (sin x - tan x)=(sin x cdot sin^2x)/(sinx(1-1/cosx))=sin^2x/(1-1/cosx)# #=((1-cos^2x)cosx)/(cosx-1)=-((1-cosx)(1+cosx)cosx)/(1-cosx)# #=-(1+cosx)cosx# then #lim_{x->0}(sin^3 x )/ (sin x - tan x)=lim_{x->0}(-(1+cosx)cosx) = -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 13436 views around the world You can reuse this answer Creative Commons License