estimating error Taylor polynomials

I have been asked to do the following:

Suppose that f is a function with the property that | | 3 for all n and for all x on [-1,1].

a. Estimate the error if the Taylor polynomial (x) (in powers of x) with n=4 is used to approximate f( ).

b. Find the least positive integer n such that (x) (in powers of x) will approximate f on [-1,1] to within .001.

I don't know where to start on this problem. I have no f(x) to work with so what do I do?

Re: estimating error Taylor polynomials

Use where is between and .

Re: estimating error Taylor polynomials

Quote:

Originally Posted by

**FernandoRevilla** Use

where

is between

and

.

Do I substitute in for x? If so, I end up with .

Or do I substitute in for ? Which gives me .

In either case, is it possible to get a number as a value for the error with the information I've been given?

Re: estimating error Taylor polynomials

.

Re: estimating error Taylor polynomials

Quote:

Originally Posted by

**FernandoRevilla** .

The error for is .0007813 and the error for is .007813, so n must be equal to 4 to remain within .001.

Thank you.