Solution Found!
Solution: Remainder terms Find the remainder term R„ in the
Chapter 7, Problem 44E(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.
\(f(x)=\cos x ; a=\pi / 2\)
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.
\(f(x)=\cos x ; a=\pi / 2\)
ANSWER:Solution 44E
Step 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.