Assume that f is a function with |f^(n)(x)|<or= 1 for all n and all real x. (The sine and cosine functions have this property.
Find the least integer n for which you can be sure that Pn(2) approximates f(2) within 0.001.
Thanks for the help!
Expanding about , and using the Lagrange form of the remainder I get:
so the required is the smallest positive integral solution of:
Now expanding about you will requre only one term, that is is exact when expansion is about .