Question Number 101977 by Ar Brandon last updated on 05/Jul/20

Given 2 functions, f and g, n-times derivable within the open interval, R and verify the property f(x_0 )=f^((k)) (x_0 )=0 , g(x_0 )=g^((k)) (x_0 )=0 , ∀k∈{1,2,...,n−1} Show that lim_(x→x_0 ) ((f(x))/(g(x)))=((f^((n)) (x_0 ))/(g^((n)) (x_0 )))