Calculus Applets 

When using a Taylor polynomial of degree n centered at c to approximate the value of a function f at x, there is an error because the polynomial does not exactly mimic the function (unless, of course, f is a polynomial of degree less than or equal to n). We can bound this error using the Lagrange remainder (or Lagrange error bound). The remainder is: where M is the maximum of the absolute value of the (n + 1)th derivative of f on the interval from x to c. The error is bounded by this remainder (i.e., the absolute value of the error is less than or equal to R). Note that R depends on how far x is away from c, how big n is, and on the characteristics of f.
Try the following:
This work by Thomas S. Downey is licensed under a Creative Commons Attribution 3.0 License.
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