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**1. The problem statement, all variables and given/known data**

Show that lim(h-->0) [f(x+h)-2f(x) + f(x-h)]/h^2

is equal to f''(x) for any given value of x where the second derivative exists.

I'm supposed to use L'Hopitals rule for this problem. I did and got

[f(x+h)-f(x-h)]/2h

Now I am stuck. I thought about adding and subtracting say f(x) but don't see how that solves to f''(x)