Read the result
Each extra term adds one more derivative at the centre. The approximation is strongest near that centre.
Taylor and approximation
Taylor Series Centre Explorer
Build a Taylor polynomial around a chosen centre and compare it with the true function.
Formula
T_n(x)=sum f^(k)(a)(x-a)^k/k!
Result
Worked substitution
Taylor approximations are local. Moving the target far from the centre makes the neglected terms matter more.
Where it helps
Use it for local approximations, series checks, and understanding why tangent and quadratic models work.
Common slip
A Taylor series about a = 0 is Maclaurin. Changing the centre changes every coefficient.
Try it
Use e^x at a = 0, then move the centre to a = 1 and compare the error near x = 1.