Taylor Series Calculator
Calculate Taylor and Maclaurin series expansions with approximation values and error analysis.
Input Parameters
a=0 gives Maclaurin series
Taylor Approximation of sin(x)
0.8414682540
Actual Value
0.8414709848
Absolute Error
2.7308e-6
Series Terms
n=0: 0.0000e+0
n=1: 1.0000e+0
n=2: 0.0000e+0
n=3: -1.6667e-1
n=4: 0.0000e+0
n=5: 8.3333e-3
n=6: 0.0000e+0
n=7: -1.9841e-4
n=8: 0.0000e+0
Convergence
Good convergence
Taylor Series
Formula
f(x) = Σ f⁽ⁿ⁾(a)/n! × (x-a)ⁿ
Where a is the center of expansion
Common Series
- eˣ = 1 + x + x²/2! + x³/3! + ...
- sin(x) = x - x³/3! + x⁵/5! - ...
- cos(x) = 1 - x²/2! + x⁴/4! - ...