Slide 11.12.pptx - Lagrange Remainder Definition Assume...

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Lagrange Remainder
Lagrange Error v.s Error in Alternating SeriesLagrange Remainder can be used with any Taylor series. It doesn’t matter if the series is alternating and decreasing.With Lagrange Remainder:To use Lagrange Remainder, the maximum value of f(n+1)(c) must be known.
Using Lagrange RemainderThe third-degree Taylor polynomial of the four-time differentiable function f(x) around x = 2 is , given that |f(4)(x)| ≤ 3 for all x in the interval [1.5,2].a) Use this series to approximate f(1.5) and find the maximum error in the approximationb) Explain why f(1.5) ≠ -5.
Using Lagrange Remainder. If |f(4)(x)| ≤ 1.5 for all x in the interval [0,0.4], what is the maximum error for f(0.4) using this third degree approximation
Using Lagrange RemainderLet a function , and let P(x) is the third degree Taylor polynomial for f about x = 0. What is the maximum value of ?

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