Lagrange Error Bound Calculator
The Lagrange Error Bound Calculator estimates the maximum error of a Taylor polynomial approximation. Enter the bound on the (n+1)th derivative, the point x, the center a, and the degree n.
Formula
|Rₙ(x)| ≤ M · |x − a|^(n+1) ÷ (n+1)!
- M is an upper bound on the (n+1)th derivative between a and x.
- The bound shrinks quickly as the degree n grows.
M=1, x=1, a=0, n=4
Inputs
- Max of (n+1)th Derivative (M): 1
- x: 1
- Center a: 0
- Degree n: 4
1 · 1⁵ ÷ 5! = 1/120 ≈ 0.00833.
Frequently asked questions
What is the Lagrange error bound?
An upper limit on the error when approximating a function by its Taylor polynomial of degree n.