(a)
To Find: Taylor polynomials up to degree 6
(a)
Answer to Problem 1E
Taylor Polynomial of degree 6 is
Explanation of Solution
Given information:
f(x)=cosx centered at a=0
Formula Used:
Taylor Polynomials
Calculation:
Taylor polynomials up to degree 6 for f(x)=cosxcentered at a=0
Taylor Polynomial of degree 6 is
To Find: f(x) and these polynomials at x=π/4,π/2,π
Answer to Problem 1E
Taylor Polynomial of degree 6 is
Explanation of Solution
Given information:
f(x)=cosx and polynomials
Calculation:
x | f | T0 | T2 | T4 | T6 |
π\4 | 0.707 | 1 | 0.691 | 0.707 | 0.707 |
π\2 | 0 | 1 | -0.233 | 0.020 | -0.0009 |
π | -1 | 1 | -3.934 | 0.123 | -1.211 |
(c)
How the Taylor polynomials converge to f(x)
(c)
Answer to Problem 1E
As n increase, Tn is a good approximation to f(x) on a larger and larger interval
Explanation of Solution
Given information:
f(x)=cosx and polynomials
Calculation:
As n increase, Tn is a good approximation to f(x) on a larger and larger interval
Chapter 8 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning