Science:Math Exam Resources/Courses/MATH100/December 2015/Question 11 (a)
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Question 11 (a) 

If the second degree Maclaurin polynomial for is , find the second degree Maclaurin polynomial 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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Recall that the second degree Maclaurin series of the function has the following form:

Hint 2 

Use product rule to find the coefficients in the series given in Hint 1. 
Hint 3 

From the given Maclaurin series for the function , how can you find ? 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. By Hint(1) and (2), we need to apply product rule to find the coefficients for the series for given by .
Similarly applying product rule to we have:
Therefore; and .
to see that and which gives
and . Substituting these into the very first formula gives:
