- #1

- 800

- 8

## Homework Statement

The Taylor series for f(x) = ln(sec(x)) at a = 0 is ##Σ_{n=0}^{∞} c_n x^n##.

(a) Find the first few coefficients. (I don't need help for this part.)

(b) Find the exact error in approximating ln(sec(-0.1)) by its fourth-degree Taylor polynomial at a = 0.

## Homework Equations

E(x) = f(x) - ##P_n (x)##, or in this case, E(-0.1) = f(-0.1) - ##P_4 (-0.1)##

## The Attempt at a Solution

I found the cofficients of each term of the polynomial, but I don't feel it's necessary to show you how I did that, since you can just confirm that I'm right by looking here.:

http://www.wolframalpha.com/input/?i=ln(sec(x))+maclaurin+polynomial

If I'm correct, for this problem, the error is the difference between the function and the 4th degree polynomial.:

E(-0.1) = f(-0.1) - ##P_4 (-0.1)## = ln(sec(-0.1)) – (1/2*0.1^2+1/12*0.1^4) = 2.2289901

__9757457996644__E-8 ≠ 2.2289901

__8157481__E-8

Notice how my answer (which is the one on the left-hand side) differs slightly from the correct answer (which is the one on the right-hand side) of the problem.

Where is this small disagreement in error/remainder values coming from?

Any input would be greatly appreciated!