Use our free Lagrange Error Bound Calculator to precisely determine the maximum possible error when approximating a function with its Taylor polynomial. Understand Taylor series remainder estimation easily and verify the accuracy of your series approximations.
Formula:
The Lagrange Error Bound (Rn(x)) for an n-th degree Taylor polynomial centered at 'a' is given by:
|Rn(x)| ≤ M ⋅ |x - a|n+1 / (n+1)!
Where:
- Rn(x): The remainder (or error) for the n-th degree Taylor polynomial. This is the value we are calculating.
- M: An upper bound for the absolute value of the (n+1)-th derivative of the function, |f(n+1)(c)|, on the interval between 'a' and 'x'. You must determine this value based on your function.
- x: The specific point at which the function is being approximated.
- a: The center of the Taylor series (the point around which the series is expanded).
- n: The degree of the Taylor polynomial used for the approximation.