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Approximations with Taylor polynomialsa. Use
Chapter 7, Problem 25E(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 \(e^{-0.15}\) using \(f(x)=e^{-x}\) and \(p_{2}(x)=1-x+x^{2} / 2\).
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 \(e^{-0.15}\) using \(f(x)=e^{-x}\) and \(p_{2}(x)=1-x+x^{2} / 2\).
ANSWER:Solution 25EStep 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) +