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Taylor / Maclaurin Series

Expand f(x) around a point to order n.

Input
Series

Enter function.

Technical Description & Theory

What is Taylor Series Calculator and Why it Matters?

Taylor expansions approximate smooth functions by polynomials, enabling local analysis and numerical methods.

Mathematical Formula and Theory

Tₙ(x) = Σ_{k=0}^n [f^{(k)}(a)/k!] (x−a)^k.

How to Use This Calculator - Step by Step

  • Enter f(x), center a, and order n.
  • Click Expand.

Solved Example with Full Calculation

exp(x) about 0 to order 4: 1 + x + x²/2 + x³/6 + x⁴/24.