# Thread: Taylor Polynomials Approx. Error

1. ## Taylor Polynomials Approx. Error

Hello. I have the following problem:

Let $f(x) = -0.5 cos(2x)$

Determine the Taylor Polynomial at x = 0

I have : $f(x) = -0.5 + x^2$ which should be correct

Now i have to show that the approx. Error in the Intervall [-0.1;0.1] is smaller than $10^{-4}$ How do i do that ? I have a formula for Langrage´s Rest but not sure how to apply it here

Edit: I should mention that we have to evaluate the polynomial to the 3rd term

2. The error will be less than the first non-calculated term. So calculate the next term and work out its largest possible value. If my mental arithmetic is correct it will be:
$|\frac 8 {4!} (0.1)^4|<10^{-4}$