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11.1 Approximating Functions with Polynomials

11.1 Approximating Functions with Polynomials. Math 6B Calculus II. Taylor Polynomial. The n th -order Taylor Polynomial is the first n terms of the Taylor series. Remainder in a Taylor Polynomial.

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11.1 Approximating Functions with Polynomials

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  1. 11.1 Approximating Functions with Polynomials Math 6B Calculus II

  2. Taylor Polynomial • The n th-order Taylor Polynomial is the first n terms of the Taylor series.

  3. Remainder in a Taylor Polynomial • Let be a Taylor polynomial of order n for f . The remainder in using to approximate f at the point x is

  4. Taylor’s Theorem • Let f have continuous derivatives up to on an open interval I containing a. For all x in I. where is the n-th order Taylor polynomial for f centered at a, and the remainder is for some point c between x and a.

  5. Taylor’s Inequality

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