Science:Math Exam Resources/Courses/MATH101/April 2007/Question 01 (j)
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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 . 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

The Maclaurin series for is

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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. 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. 