# Calculate the Taylor expansion of a function

## Calculus taylor_series_expansion

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### Function : taylor_series_expansion

#### Summary :

The taylor series calculator allows to calculate the Taylor expansion of a function.

Taylor_series_expansion online

#### Description :

The online taylor series calculator helps determine the Taylor expansion of a function at a point. The Taylor expansion of a function at a point is a polynomial approximation of the function near that point. The degree of the polynomial approximation used is the order of the Taylor expansion.

# Usual function Taylor expansion

The calculator can calculate Taylor expansion of common functions.

For example, to calculate Taylor expansion at 0 of the cosine function to order 4, simply enter taylor_series_expansion(cos(x);x;0;4) after calculation, the result is returned.

To calculate dl at 0 of the exponential function to order 5, simply enter taylor_series_expansion(exp(x);x;0;5), , after calculation, the result is returned.

# Calculation of the Taylor series expansion of any differentiable function

To calculate Taylor expansion at 0 of the f: x->cos(x)+sin(x)/2, to order 4, simply enter taylor_series_expansion(cos(x)+sin(x)/2;x;0;4) after calculation, the result is returned.

The taylor series calculator allows to calculate the Taylor expansion of a function.

#### Syntax :

taylor_series_expansion(function;variable;value;order),
• function: the function at which the expansion is researched,
• variable: the variable used for the expansion,
• value: the point at which the expansion is researched,
• order: order of the expansion.

#### Examples :

taylor_series_expansion(cos(x);x;0;4), returns (x^4)/24+(-x^2)/2+1

Calculate online with taylor_series_expansion (Calculate the Taylor expansion of a function)