Home | 18.01 | Chapter 6 | Section 6.1

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1. One can apply the approximation given by the first k terms of this series to any function whose first k derivatives exist between x and a.    

The bounds derivable on the accuracy of these approximations apply to all such functions.

 2. Wherever the Taylor series converges, its value is that of the function. It can be used to determine the value of the function even where it diverges.