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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-

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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 )))
Given2functions,fandg,n−timesderivablewithintheopeninterval,Randverifythepropertyf(x0)=f(k)(x0)=0,g(x0)=g(k)(x0)=0,∀k∈{1,2,…,n−1}Showthatlimx→x0f(x)g(x)=f(n)(x0)g(n)(x0)

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