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.