Problem 5E

How is the remainder in a Taylor polynomial defined?

Solution 5E

Step 1:

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) = .

That is ,

Taylor series; f(a) +++............

Taylor polynomial ; f(a) ++

Remainder term ;(x) = ++………….

| (x)| = | |.