Taylor Series Calculator
Common Taylor/Maclaurin Series
Expand a common function into its Maclaurin series (centered at 0)
Taylor Series (centered at a)
Approximate f(x) = eˣ using Taylor series centered at point a
Formula
f(x) = Σ f⁽ⁿ⁾(a)/n! · (x-a)ⁿ | Maclaurin: a = 0 | eˣ = Σ xⁿ/n!
Frequently Asked Questions
What is a Taylor series?
A Taylor series represents a function as an infinite sum of terms calculated from the function's derivatives at a single point. f(x) = Σ f⁽ⁿ⁾(a)/n! · (x-a)ⁿ. When centered at a=0, it's called a Maclaurin series.
What is the difference between Taylor and Maclaurin series?
A Maclaurin series is simply a Taylor series centered at a = 0. Both are power series expansions, but Maclaurin uses derivatives evaluated at x = 0.
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