Find Taylor polynomial for f(x) = √x about x = 4; find error bound.

[eagle2020]

Help with these 2 problems please:
Let f(x) = √x
(a) Find the second-degree Taylor polynomial P2(x) for f(x) about x = 4.
(b) Provide a bound for the error in the approximation √5 ≈ P2(5). Express your bound as arational number. (You do not need to compute P2(5)).

 

[j-astron]

Do you know how to do a Taylor series expansion? Can you start by maybe writing out the general equation for a Taylor series expansion?

Hint: a second-order Taylor polynomial is what you get if you only keep the terms in the Taylor series expansion up to second-order and throw out all the higher ones.