How do you evaluate the limit #(sqrt(x+2)-sqrt(2-x))/x# as x approaches #0#? Calculus Limits Determining Limits Algebraically 1 Answer Ratnaker Mehta Aug 16, 2016 #sqrt2/2#. Explanation: Reqd. Limit#=lim_(xrarr0) (sqrt(x+2)-sqrt(2-x))/x# #lim_(xrarr0) (sqrt(x+2)-sqrt(2-x))/x xx (sqrt(x+2)+sqrt(2-x))/(sqrt(x+2)+sqrt(2-x))# #lim_(xrarr0) (x+2-2+x)/(x(sqrt(x+2)+sqrt(2-x))# #lim_(xrarr0) (2cancelx)/(cancelx(sqrt(x+2)+sqrt(2-x))# #=2/(sqrt2+sqrt2)# #=2/(2sqrt2)# #=sqrt2/2#. 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 27905 views around the world You can reuse this answer Creative Commons License