Taylor series: f(x) = Σ f⁽ⁿ⁾(a)/n! · (x−a)ⁿ. Maclaurin series: a=0. Key expansions: eˣ = Σxⁿ/n!, sin(x) = Σ(−1)ⁿx²ⁿ⁺¹/(2n+1)!, cos(x) = Σ(−1)ⁿx²ⁿ/(2n)!. The more terms, the better the approximation near the center.
How to Use
Select a function:
- Function: Choose from presets
- x value: Where to evaluate
- Terms: Number of terms
Common Series
- eˣ = 1 + x + x²/2! + x³/3! + ...
- sin(x) = x − x³/3! + x⁵/5! − ...
- cos(x) = 1 − x²/2! + x⁴/4! − ...
Convergence
eˣ, sin, cos converge for all x. ln(1+x) converges for −1 < x ≤ 1. 1/(1−x) converges for |x| < 1.
Step-by-Step Instructions
- 1Select a function.
- 2Enter x value.
- 3Choose number of terms.
- 4View term-by-term expansion.
- 5Check approximation accuracy.