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Remainder terms Find the remainder term R„ in
Chapter 7, Problem 45E(choose chapter or problem)
Remainder terms Find the remainder term \(R_{n}\), in the nth order Taylor polynomial centered at a for the given functions. Express the result for a general value of n.
\(f(x)=\sin x ; \quad a=\pi / 2\)
Questions & Answers
QUESTION:
Remainder terms Find the remainder term \(R_{n}\), in the nth order Taylor polynomial centered at a for the given functions. Express the result for a general value of n.
\(f(x)=\sin x ; \quad a=\pi / 2\)
ANSWER:Solution 45EStep 1:In this problem we have to find out the remainder term(R) , in the nth order polynomial f(x) = centered at a = .Remainder in a taylor polynomial() ;Suppose that f is n+1 times differentiable and let denote the difference between f(x) and the Taylor polynomial of degree n for f(x) centered at a. Then, (x) = f(x) - (x) = .| (x)| = | |.That is , Taylor series; f(a) +++............Taylor polynomial ; f(a) ++Remainder term ;(x) = ++………….Where c lies between x to a.