How do you find the limit of # [ x (cot^2 x)] / [(csc x) +1]# as x approaches 0? Calculus Limits Determining Limits Algebraically 1 Answer Eddie Sep 7, 2016 #= 1# Explanation: #lim_(x to 0) [ x cot^2 x] / [csc x +1]# #=lim_(x to 0) [ x cot^2 x] / [csc x +1] * (csc x - 1)/(csc x - 1)# #=lim_(x to 0) [ x cot^2 x (csc x - 1)] / [csc^2 x - 1]# #=lim_(x to 0) [ x cot^2 x (csc x - 1)] / [cot^2 x ]# #=lim_(x to 0) x (csc x - 1)# #=lim_(x to 0) x /(sin x) - x# and because #lim_(alpha to 0) alpha /(sin alpha) = 1# #= 1 - 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 3006 views around the world You can reuse this answer Creative Commons License