Taylor Series Approximation JavaScript Simulation Applet HTML5
The Taylor Series is a generalised polynomial approximation to a function, centered around x = a, for any real number a.
In this simulation (link here), you can choose a function to approximate with the Taylor Series from the combo box provided. However, this is technically not a series, as the terms do not go indefinitely.
Beside the combo box for selecting the function, there is a set of 10 checkboxes, each of them corresponding to a certain degree of approximation. The degree of the polynomial approximation is shown by the number beside the checkbox. When each box is checked, the graph of the polynomial corresponding to the degree denoted by the checkbox is made visible; unchecking it will make it invisible.
The available functions are as follows:
- Gaussian: y = e^-(x^2)
- y = sin(x)
- y = sin(x)^2
- y = sin(x)/x
- sin(x)/x Quadratic: y = [sin(x)/x]^2
- y = x^7
- y = e^x
At the top of the simulation, the full 9th degree polynomial approximation for the function at the point denoted by the square in the graph is shown, and will automatically change when the point is moved. Likewise, the graphs of the different polynomial approximations will also adjust accordingly.
In this simulation (link here), you can choose a function to approximate with the Taylor Series from the combo box provided. However, this is technically not a series, as the terms do not go indefinitely.
Beside the combo box for selecting the function, there is a set of 10 checkboxes, each of them corresponding to a certain degree of approximation. The degree of the polynomial approximation is shown by the number beside the checkbox. When each box is checked, the graph of the polynomial corresponding to the degree denoted by the checkbox is made visible; unchecking it will make it invisible.
The available functions are as follows:
- Gaussian: y = e^-(x^2)
- y = sin(x)
- y = sin(x)^2
- y = sin(x)/x
- sin(x)/x Quadratic: y = [sin(x)/x]^2
- y = x^7
- y = e^x
At the top of the simulation, the full 9th degree polynomial approximation for the function at the point denoted by the square in the graph is shown, and will automatically change when the point is moved. Likewise, the graphs of the different polynomial approximations will also adjust accordingly.
