L'Hopital's Rule finding the limit

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Can you tell me if my answer is correct use L'Hopital's Rule to find the limits of the following

lim as h->0 of

( f(x+h)-2f(x)+f(x-h) )/h^2

here f(x) is not given as h->0 is plugged in first it comes out as 0

if i differentiate i get

( f'(x+h)+f'(x-h) )/2h and when 0 is plugged it is inf

so i differentiate it again and do it

so i get ( f''(x+h)+f''(x-h) )/2 and when 0 is plugged in i get f''(x)

so is this right as after i differentiate once i get inf, is that supposed to happen

edited 1 min ago

David Heffernan

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asked 2 mins ago

Sahan J

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L'Hopital's Rule finding the limit