How do you find the limit of #(x-tanx)/x^3# as x approaches 0? Calculus Limits Determining Limits Algebraically 1 Answer Massimiliano Apr 29, 2015 In this way: #lim_(xrarr0)(x-tanx)/x^3=#Hospital#=lim_(xrarr0)(1-1-tan^2x)/(3x^2)=# #=lim_(xrarr0)-sin^2x/(3x^2cos^2x)=lim_(xrarr0)-(sinx/x)^2*1/(3cos^2x)=# #=-1^2*1/(3*1)=-1/3#. 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 31768 views around the world You can reuse this answer Creative Commons License