MATH103 April 2011
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Question 07 (a)
Find the first three non-zero terms of the Taylor series for
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Recall that the Taylor series for a function about is given by
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The first three derivatives of are
When we evaluate these at we get , , . Hence, the first few terms of the Taylor series for about are
These are the first three non-zero terms.
(Note: It is actually pretty easy to obtain the entire Taylor series anyway. For any we can show that Hence, and therefore, )
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