- 66

- 0

**1. The problem statement, all variables and given/known data**

Find the maximum error in approximating cos(x) by its Taylor polynomial of order 2 on the

interval [

−.25, .25]. Justify your answer using the Remainder Estimation Theorem.

**2. Relevant equations**

|R3(x)<=M/3! |x|^3

**3. The attempt at a solution**

|R3(x)<=M/3! |x|^3 Plugging in the 3 is easy enough, but I don't understand where the M comes from. What is M here? I initally thought it might be the value of the 4th taylor polynomial, but that would make the remainder less than or = zero, right?