Prove by induction that for all k, dj dxj (x a)k k! = k(k 1)(k j + 1)(x a)kj k! dj dxj
Chapter 8, Problem 70(choose chapter or problem)
Prove by induction that for all k, dj dxj (x a)k k! = k(k 1)(k j + 1)(x a)kj k! dj dxj (x a)k k! x=a = 1 for k = j 0 for k = j Use this to prove that Tn agrees with f at x = a to order n.
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