Calculus
Taylor Series Calculator
Lets users solve and check taylor series instantly with formula, steps and examples — no manual math.
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Your result
Taylor polynomial
1 + 1·(x−0)^1 + 0.5·(x−0)^2 + 0.1667·(x−0)^3 + 0.0417·(x−0)^4
Taylor polynomial (5 terms) ≈ 1 + 1·(x−0)^1 + 0.5·(x−0)^2 + 0.1667·(x−0)^3 + 0.0417·(x−0)^4; value at x=1 ≈ 2.7083 (actual 2.7183).
Approx value at x
2.7083
Actual f(x)
2.7183
About this calculator
The Taylor series expands f(x) around a as Σ f⁽ⁿ⁾(a)/n! · (x−a)ⁿ. Coefficients come from numeric derivatives. More terms improve accuracy near the center a.
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