Taylor polynomials Find the nth-order Taylor polynomial for the following functions with the given center point a.

f(x) =cosx, n = 2, a = π/4

Solution 6RE

Step 1:

In this problem we have to find the -order Taylor polynomial for function with the given center point a=.

Taylor series is given by

In our case,

That is

So, what we need to do to get desired polynomial is to calculate derivatives, evaluate them at the given point and plug results into given formula.

Step 2:

Then

Then

Then