Taylor Series Calculator

Calculate Taylor series expansions and polynomial approximations for functions like sin, cos, exp, and ln.

Function Parameters

Function

Evaluation Point (x)

Number of Terms: 10

f(x) = Σ f^(n)(a)/n! × (x-a)^n

Taylor Approximation (10 terms)

0.8414709848

Exact Value

0.8414709848

Absolute Error

0.0000e+0

Relative Error

0.000000%

n=0: + x^1/1!1.000000e+0

n=1: - x^3/3!-1.666667e-1

n=2: + x^5/5!8.333333e-3

n=3: - x^7/7!-1.984127e-4

n=4: + x^9/9!2.755732e-6

n=5: - x^11/11!-2.505211e-8

n=6: + x^13/13!1.605904e-10

n=7: - x^15/15!-7.647164e-13