MAT-261 Lecture 24: 8.8 Applications of Taylor Polynomials Notes
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8. 8 applications of taylor polynomials notes: sterling. Provide a generalization to each of the key terms listed in this section. Taylor"s inequality occurs when you let f n+1 be continuous while the following is between both a and x: If that is the case, then the following would be its outcome: (cid:12)(cid:12)f n+1(cid:12)(cid:12) m. It would be best if you let the following occur: If that is the case, then the following would be the limit for c, which can be any number: Rn (x) = f (x) tn (x) lim n (rn (c)) = 0. If that is the general case for both, then the following would be equivalent to its own taylor series while it"s at c: f (x) It that is the actual case, then c for anything in the following interval or even on the real number line: (a r, a + r) X n=0 f n (a) n! (x a)n.
