Taylor polynomial
The app builds the Taylor (at 0 the Maclaurin) polynomial of a given degree: a table of the derivatives at the point, substitution into the formula and the remainder in Lagrange form. It can also find the degree itself – the smallest one for which the error at a given point or on an interval stays below a given bound. The graph shows the function and the polynomial; a slider changes the degree so you can see the approximation improve.
How to enter it
taylor(sin x, 0, 5) | The function, the point and the degree. |
maclaurin(e^x, 4) | The Maclaurin polynomial – the point is 0. |
taylor(e^x, 0, error=0.001, x=0.5) | The degree by the error at the point x (on an interval enter r=… instead of x). |
ln(1 + x) | A function with the “Taylor polynomial” chip – fill in the point, the degree or the accuracy there. |
Examples
A polynomial of degree 4 with the remainder.
Input:
taylor(ln(1 + x), 0, 4)
The degree by the required accuracy – an approximate value of e^0.5.
Input:
taylor(e^x, 0, error=0.001, x=0.5)
