テイラー級数計算機

共有リンク

はじめに

Taylor Series Calculator — Compute Taylor/Maclaurin series coefficients for common functions. Enter Function, Number of terms to get an instant, accurate result.

計算式

Generates the Maclaurin (Taylor-at-0) series coefficients for eˣ, sin(x), or cos(x) up to the requested number of terms, using each function's known term pattern (e.g. sin(x) alternates 0, x/1!, 0, −x³/3!, 0, x⁵/5!, …).

ステップごとの説明

Enter the Function.
Enter the Number of terms.
Click Calculate to see your result instantly.

実例

Example: With Function = exp, Number of terms = 5, the Taylor Series Calculator gives Function: exp, Coefficients: 1, 1, 0.5, 0.1667, 0.0417.

よくある質問

Is this expanded around x = 0?

Yes — this generates the Maclaurin series, which is the Taylor series specifically centered at x = 0.

Which functions are supported?

eˣ, sin(x), and cos(x).

What inputs does the Taylor Series Calculator need?

You'll need to provide: Function, Number of terms. All fields use sensible defaults, so you can see a working example immediately and then adjust the values to match your own numbers.

How accurate is the Taylor Series Calculator?

The Taylor Series Calculator applies the formula exactly as calculated — Generates the Maclaurin (Taylor-at-0) series coefficients for eˣ, sin(x), or cos(x) up to the requested number of terms, using each function's known term pattern (e.g. sin(x) alternates 0, x/1!, 0, −x³/3!, 0, x⁵/5!, …). — so results are precise for the inputs you provide. Accuracy depends on entering correct, realistic input values.

Is the Taylor Series Calculator free to use?

Yes, the Taylor Series Calculator is completely free, requires no signup, and runs instantly in your browser.