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

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

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.

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.

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

See also

- Even or odd function calculator : is_odd_or_even_function. Calculator for determining whether a function is an even function and an odd function.
- Partial fraction decomposition calculator : partial_fraction_decomposition. The calculator allows a rational fraction to be broken down into simple elements.
- Derivative calculator : derivative. The derivative calculator allows steps by steps calculation of the derivative of a function with respect to a variable.
- Taylor expansion calculator : taylor_series_expansion. The taylor series calculator allows to calculate the Taylor expansion of a function.
- Properties of a numerical function : study_function. This calculator lets you study a function using the following algebraic calculation tools: derivative, antiderivative, is_odd_or_even_function, equation_tangent_line, discriminant, degree, valuation.
- Integral calculator : integral. The integral calculator calculates online the integral of a function between two values, the result is given in exact or approximated form.
- Indefinite integral calculator : antiderivative. The antiderivative calculator allows to calculate an antiderivative online with detail and calculation steps.
- Limit calculator : limit. The limit calculator allows the calculation of the limit of a function with the detail and the calculation steps.