Solution Found!
a. Find the Taylor polynomials of order n = 0, 1. and 2
Chapter 1, Problem 10RE(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.
\(f(x)=\sqrt{1+x}, a=0\); approximate \(\sqrt{1.08}\).
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.
\(f(x)=\sqrt{1+x}, a=0\); approximate \(\sqrt{1.08}\).
ANSWER:Solution 10RE
Step 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)= and a=0 is
For order
For order
For order