Taylor Series Calculator
Calculate Taylor series approximation for common functions around a given point
About this calculator
A Taylor Series Calculator computes polynomial approximations of mathematical functions around a specified point using Taylor's theorem. This powerful tool breaks down complex functions into infinite series of terms, making it invaluable for calculus students, engineers, and mathematicians who need to approximate function values or analyze function behavior. The calculator helps visualize how functions can be represented as power series, essential for numerical analysis, differential equations, and advanced mathematical modeling.
How to use
Select your desired function from the dropdown menu (sin, cos, exp, ln, etc.), enter the point around which you want the series expansion, and specify the number of terms you need. The calculator will generate the Taylor series formula and provide numerical approximations, showing each term's contribution to the final result.
Frequently asked questions
What's the difference between Taylor and Maclaurin series?
A Maclaurin series is simply a Taylor series expanded around the point x = 0. Taylor series can be centered at any point a.
How many terms should I use for accurate approximation?
More terms generally increase accuracy, but 5-10 terms often provide good approximations near the expansion point. Accuracy decreases farther from the center.
Why do some functions have infinite Taylor series?
Most smooth functions can be represented as infinite power series. The series converges to the original function within its radius of convergence.