Taylor Expansion Calculator

Taylor Expansion Calculator

Taylor Expansion Calculator

This Taylor Expansion Calculator allows you to estimate functions using Taylor Series. By inputting a function, the center point (a), and the number of terms (n), you can calculate the approximation of the function as a sum of polynomials.

What is Taylor Expansion Calculator?

A Taylor Expansion Calculator estimates the value of a function using a series expansion around a given point. By providing the function, center point (a), and number of terms, the calculator approximates the function as a sum of polynomials. It’s useful for approximating complex functions in mathematics and engineering.

What is the Formula of Taylor Expansion?

The formula for the Taylor expansion of a function f(x) around a point a is:

f(x) ≈ f(a) + f'(a)(x - a) + f''(a)(x - a)^2 / 2! + f'''(a)(x - a)^3 / 3! + ...

Advantages and Disadvantages of Taylor Expansion Calculator

Advantages:

  • Helps to approximate complex functions simply.
  • Provides a numerical estimate for the value of the function at specific points.
  • Useful in various fields such as physics, engineering, and economics.

Disadvantages:

  • Accuracy decreases as the number of terms is limited.
  • Convergence may not occur for some functions if the series does not match the function well.