MATH101 April 2006
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Question 01 (j)
Find the first three nonzero terms in the power series representation in powers of x (i.e. the Maclaurin series) for
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The Maclaurin series for is
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Starting with the Maclaurin series for , we have
Plugging in -t2, we have
Multiplying by , we have
Now integrating gives
Plugging in endpoints, we have
and so the first three nonzero terms are
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