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Lagrange Taylor Error Bound Calculator — result sheet
Estimate the Lagrange remainder bound for a Taylor polynomial from derivative bound, distance, and polynomial degree.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: |Rₙ(x)|≤M|x−a|^(n+1)/(n+1)!.
The Lagrange form gives an upper bound on the remainder when a bound M for the next derivative is valid throughout the interval between the expansion point and x.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Maximum derivative bound M — minimum 0; maximum 1.0E+100
- Distance |x−a| — minimum 0; maximum 1000000
- Taylor polynomial degree n — minimum 0; maximum 170
Worked example
| Input | Value |
|---|---|
| Maximum derivative bound M | 1 |
| Distance |x−a| | 0.5 |
| Taylor polynomial degree n | 3 |
Error bound ≤0.00260417.
Assumptions and limits
- M bounds the absolute value of the (n+1)th derivative across the required interval.
- Degree is a nonnegative whole number and distance is nonnegative.
- The output is a bound, not the signed or exact error of a particular approximation.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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