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Approximations with Taylor polynomialsa. Use
Chapter 7, Problem 26E(choose chapter or problem)
Approximations with Taylor polynomials
a. Use the given Taylor polynomial \(p_{2}\) to approximate the given quantity.
b. Compute the absolute error in the approximation assuming the exact value is given by a calculator.
Approximate \(\frac{1}{1.12^{3}}\) using \(f(x)=\frac{1}{(1+x)^{3}}\) and \(p_{2}(x)=1-3 x+6 x^{2}\).
Questions & Answers
QUESTION:
Approximations with Taylor polynomials
a. Use the given Taylor polynomial \(p_{2}\) to approximate the given quantity.
b. Compute the absolute error in the approximation assuming the exact value is given by a calculator.
Approximate \(\frac{1}{1.12^{3}}\) using \(f(x)=\frac{1}{(1+x)^{3}}\) and \(p_{2}(x)=1-3 x+6 x^{2}\).
ANSWER:Solution 26E
Step 1:
In this problem , we have to find out the approximation value by using taylor's polynomial.
The Taylor polynomial of degree n centered at x = a approximating the function f(x) is;
= f(a) +
(x-a) +
=