The proof in Exercise 70 guarantees that the Taylor polynomial and its derivatives agree with the function
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The proof in Exercise 70 guarantees that the Taylor polynomial and its derivatives agree with the function and its derivatives at x = c. Use the graphs and tables in Exercises to discuss what happens to the accuracy of the Taylor polynomial as you move away from x = c.
Data from in Exercise 70
Let Pn(x) be the nth Taylor polynomial for ƒ at c. Prove that Pn (c) = ƒ(c) and P(k)(c) = ƒ(k) (c) for 1 ≤ k ≤n.
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