How do you find the limit of #x tan (8/x) # as x approaches infinity? Calculus Limits Determining Limits Algebraically 1 Answer Ratnaker Mehta Jan 15, 2017 #8#. Explanation: Let #1/x=theta," so that, as "xrarroo, theta rarr0#. Also, we know that, #lim_(thetararr0) tantheta/theta=1#. #:." The Reqd. Limit="lim_(theta rarr 0) (tan8theta)/theta# #=lim_(theta rarr 0) (tan8theta)/(8theta)(8)# #=lim_(8thetararr0) (tan8theta)/(8theta)(8)# #=(1)(8)=8# 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 4535 views around the world You can reuse this answer Creative Commons License