Question #b94eb Calculus Limits Determining Limits Algebraically 1 Answer Alan P. Feb 19, 2017 #lim_(trarr0) (sin(t))/(tan(t))=color(green)1# Explanation: #tan(t)=sin(t)/cos(t)# (provided #cos(t)!=0#) #rArr (sin(t))/(tan(t))=cancel(sin(t)) xx (cos(t))/(cancel(sin(t)))=cos(t)# #lim_(trarr0) cos(t)=cos(0) = 1# 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 887 views around the world You can reuse this answer Creative Commons License