Taylor Series Calculator
Generate Taylor series expansions for mathematical functions
Taylor Series Formula
f(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)²/2! + f'''(a)(x-a)³/3! + ...
f(x) = Σ[f⁽ⁿ⁾(a)(x-a)ⁿ/n!] for n=0 to ∞
Applications
Mathematics
- Function approximation
- Numerical analysis
- Solving differential equations
- Series convergence studies
Engineering
- Signal processing
- Control systems
- Physics simulations
- Optimization problems
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. It allows us to approximate complex functions with polynomials, making them easier to analyze and compute.