Calculus
Advanced

Taylor Series

Expands a function as an infinite polynomial around a.

Formula

f(x)=∑n=0∞f(n)(a)n!(x−a)nf(x) = \sum_{n=0}^{\infty}\frac{f^{(n)}(a)}{n!}(x-a)^n

Variables

aExpansion point
nTerm index

Example

Near a=0, cos x ≈ 1 − x²/2 + x⁴/24 — the first few Taylor terms.

Did You Know?

Taylor series let a computer compute sin, cos, and e^x using nothing but addition and multiplication.

seriestaylorapproximation