Let *f(x)* be a function whose first *n* derivatives exist on some interval *I*. Suppose that we wish to approximate *f(x)* near the value *x = c* in *I* using a degree *n* polynomial *p** _{n} (x)* so that

**Equation D.1. **

whenever *x* is small. The derivatives of *p** _{n}(x)* evaluated at

**Equation D.2. **

We can determine the coefficients a_{i} by requiring that

**Equation D.3. **

The polynomial *p*_{n} *(x)* is thus given by

**Equation D.4. **

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