Estimate the maximum remainder error for a Taylor polynomial using the Lagrange bound.
Last updated: June 2026 | By Patchworkr Team
The Lagrange error bound gives a safe upper limit on the Taylor remainder term.
If M = 2, n = 3, x = 1, and a = 0, then the result is 0.083333.
Why must n be an integer?
The Taylor remainder uses the (n + 1)th derivative and the factorial (n + 1)! term.
Can the bound be zero?
Yes. If x = a, then |x - a|^(n + 1) = 0 and the bound becomes 0.
Does the tool accept scientific notation?
Yes. Inputs like 1e-3 are accepted as long as they are finite real numbers.
Why reject very large n?
The factorial term can overflow, so the calculator stops before producing an unreliable result.
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