MATH101 April 2007
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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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We apply for 'x in the Maclaurin series for cos(x) to get
Now we multiply by t to get
Now we integrate to get
Applying the endpoints gives
and so the first three nonzero terms are
completing the question.
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