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Question 10 (a) 

FullSolution Problem. Justify your answer and show your work. Full simplification of numerical answers is required unless explicitly stated otherwise. Find the first 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 

A Maclaurin polynomial is a Taylor polynomial centred at (i.e, ). 
Hint 2 

At the point where the approximation is made, the first degree Taylor/Maclaurin polynomial has the same first derivative as the function which it approximates (i.e., ). 
Hint 3 

Recall that the equation of a first degree Taylor polynomial centred at is given by and that for a Maclaurin polynomial, 
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. The equation of the first degree Maclaurin polynomial for f is . For we have . To find , we differentiate using the chain rule:
