Taylor Series Expansion Including the Error Term. Polynomials. ’s TAYLOR POLYNOMIALS AND SERIES, INCLUDING THE ERROR TERM Applications to the approximations of functions; formulae for the error term, both in terms of the value of the derivative at an intermediate point, and in terms of (n+1)th an integral of the derivative. (n+1)th Example 1 Find the first four polynomials for about ’s Graphing the above: These polynomials produce their best approximations of near the point ln(x) Example 2 Find the first seven Maclaurin polynomials for Only the odd powers appear explicitly: Because of the zero terms, each even order Maclaurin polynomial (after is the same as the preceding odd order Maclaurin polynomial. Graph: Example 3 Repeat for up to . Use . Draw the graph of and the Maclaurin polynomials on the same set of axes on your graphics calculator.
Taylor Series Expansion Including the Error Term. ’s Polynomials. TAYLOR POLYNOMIALS AND SERIES, INCLUDING THE ERROR TERM Applications to the approximations of functions; formulae for the error term, both in terms of the value of the (n+1)th derivative at an intermediate point, and in terms of an integral of the (n+1)th derivative. Example 1 Find the first four ’s polynomials for about Graphing the above: These polynomials produce their best approximations of ln(x) near the point Example 2 Find the first seven Maclaurin polynomials for Only the odd powers appear explicitly: Because of the zero terms, each even order Maclaurin polynomial (after is the same as the preceding odd order Maclaurin polynomial. Graph: Example 3 Repeat for up to . Use . Draw the graph of and the Maclaurin polynomials on the same set of axes on your graphics calculator.
Taylor-Series-Expansion-Including-the-Error-Term-1.docx