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

taylor_series_expansion online

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
- Calculation of the Taylor series expansion of any differentiable function

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.

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.

- 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.

See also :

- Antiderivative calculator : antiderivative_calculator. The antiderivative calculator allows to calculate an antiderivative online with detail and calculation steps.
- Derivative calculator : derivative_calculator. The derivative calculator allows steps by steps calculation of the derivative of a function with respect to a variable.
- Integral calculator : integral_calculator. The integral calculator calculates online the integral of a function between two values, the result is given in exact or approximated form.
- Even or odd function calculator : is_odd_or_even_function. Calculator for determining whether a function is an even function and an odd function.
- Limit of a function : limit_calculator. The limit calculator allows the calculation of the limit of a function with the detail and the calculation steps.
- Partial fraction decomposition : partial_fraction_decomposition. The calculator allows a rational fraction to be broken down into simple elements.
- Calculate the Taylor expansion of a function : taylor_series_expansion. The taylor series calculator allows to calculate the Taylor expansion of a function.