Science:Math Exam Resources/Courses/MATH103/April 2011/Question 07 (a)
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Question 07 (a) 

Find the first three nonzero terms of the Taylor series for around . 
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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 

Recall that the Taylor series for a function about is given by

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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The first three derivatives of are
and
When we evaluate these at we get , , . Hence, the first few terms of the Taylor series for about are
These are the first three nonzero terms. (Note: It is actually pretty easy to obtain the entire Taylor series anyway. For any we can show that Hence, and therefore, ) 