The Taylor formula allows you to understand the behavior of a function near a certain point. In general, it looks like this:
where rn(X) – remainder n-th order:
Variants of the remainder term
rn(X) can be represented by different expressions:
- In the Lagrange form:
2. In the form of Cauchy:
Note: The formula is so named after the English mathematician Brooke Taylor, it is often used in mathematical analysis, sometimes in physics.