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Approximationsa. Find the Taylor polynomials of order n =
Chapter 1, Problem 8RE(choose chapter or problem)
Approximations
a. Find the Taylor polynomials of order n = 0, 1, and 2 for the given functions centered at the given point a.
b. Make a table showing the approximations and the absolute error in these approximations using a calculator for the exact function value.
f(x) = cos x, a = 0; approximate cos (-0.08).
Questions & Answers
QUESTION:
Approximations
a. Find the Taylor polynomials of order n = 0, 1, and 2 for the given functions centered at the given point a.
b. Make a table showing the approximations and the absolute error in these approximations using a calculator for the exact function value.
f(x) = cos x, a = 0; approximate cos (-0.08).
ANSWER:Solution 8REStep 1:The general notation of a taylor series is given by Here when a=0 the series is called maclaurin series.Here We need to find the Taylor polynomials of order n = 0, 1. and 2 for the given functions centered at the given point a.Therefore the taylor series for f(x)=cos x and a=0 is For order For order For order