How do you find the limit #(sqrt(x^2+1)-1)/(sqrt(x+1)-1)# as #x->0#?
1 Answer
Dec 13, 2016
Use a variation of the same method used for similar limits.
Explanation:
The initial form is
# = (x^2(sqrt(x+1)+1))/(x(sqrt(x^2+1)+1))#
# = (x(sqrt(x+1)+1))/(sqrt(x^2+1)+1)#
Taking the limit as
# = ((0)(1+1))/((1)+1) = 0#