Taylor Series

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Unformatted text preview: abola than it does a straight line. This suggests that it would make more sense to try and approximate this function with a function of the form p(x) = c0 + c1 (x − a) + c2 (x − a)2 DE Math 128 314 (B. Forrest)2 CHAPTER 4. Sequences and Series 4.5. Introduction to Taylor Series (You may have noticed that the form for this polynomial looks somewhat unusual. We write it this way because it will make it easier to properly encode the information we have about f (x) at x = a). In constructing the linear approximation, we encoded the value of the function and of its derivative at the point x = a. We want to again encode this local information, but we want to do more. If we can add in the second derivative, we might be able to capture the curvature of the function that was missing in the linear approximation. In summary, we would like find constants c0 , c1 , and c2 , so that 1. p(a) = f (a), 2. p (a) = f (a), 3. p (a) = f (a). It may not seem immediately obvious that we can find such constants. How...
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This document was uploaded on 03/23/2013.

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