Suppose f: J R is n times differentiable on the open interval J. Prove the formula...

 

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Suppose f: J R is n times differentiable on the open interval J. Prove the formula n f(m) (x) = lim h " (-1)"-kf(x+ kh). k k=0 h0 Note: If you want to apply l'Hopital's rule, you'll have to justify that it applies. Suppose f: J R is n times differentiable on the open interval J. Prove the formula n f(m) (x) = lim h " (-1)"-kf(x+ kh). k k=0 h0 Note: If you want to apply l'Hopital's rule, you'll have to justify that it applies.