# AP Calculus BC : Lagrange Error Bound for Taylor Polynomials

## Example Questions

### Example Question #1 : Lagrange Error

Let  be the fifth-degree Taylor polynomial approximation for , centered at .

What is the Lagrange error of the polynomial approximation to ?

Explanation:

The fifth degree Taylor polynomial approximating  centered at  is:

The Lagrange error is the absolute value of the next term in the sequence, which is equal to .

We need only evaluate this at  and thus we obtain