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Solved: Approximationsa. Find the Taylor polynomials of
Chapter 1, Problem 11RE(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.
\(f(x)=\sin x, \quad a=\pi / 4\); approximate \(\sin (\pi / 5)\).
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.
\(f(x)=\sin x, \quad a=\pi / 4\); approximate \(\sin (\pi / 5)\).
ANSWER:Solution 11RE
Step1:
Given that
f(x) = sin a, a = π/4: approximate sin (π/5).
Step2:
To find
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.
Step3:
a. The Taylor polynomials of order n = 0, 1. and 2 for the given functions centered at the given point a.
For n=0
f(a)=sin(a)
f(sin(
)
=0
For n=1