How do you find the limit of # (tan2x)/(5x)# as x approaches 0? Calculus Limits Determining Limits Algebraically 1 Answer Cesareo R. Jun 12, 2016 #lim_{x->0}tan(2x)/(5x) = 2/5# Explanation: #tan(2x)/(5x)=sin(2x)/(5x cos(2x)) = ((sin(2x))/(2x))(2/(5 cos(2x)))# so #lim_{x->0}tan(2x)/(5x) = lim_{x->0} ((sin(2x))/(2x)) xx lim_{x->0}(2/(5 cos(2x)))# Finally #lim_{x->0}tan(2x)/(5x) = 1 xx 2/5 = 2/5# 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 10617 views around the world You can reuse this answer Creative Commons License