Science:Math Exam Resources/Courses/MATH103/April 2012/Question 01 (f)
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Question 01 (f) 

Answer the following multiple choice question. Check your answer very carefully. Your answer will be marked right or wrong (work will not be considered for this problem). In the Taylor series of (about the point x = 0), the coefficient of the x^{3} term is

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 Taylor series of is the Taylor series of multiplied by x. 
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Solution 1 

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Please rate my easiness! It's quick and helps everyone guide their studies. Recall that therefore The coefficient of x^{3} term is 1/2 and so the correct answer is D. 
Solution 2 

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Please rate my easiness! It's quick and helps everyone guide their studies. If you don't remember the Taylor series about x = 0 of you can simply recompute it. Recall that the Taylor series of a function ƒ about the point x = a is For the function we have and so at a = 0 we obtain And so the Taylor series of around x = 0 is And hence the Taylor series of around x = 0 is And we can observe that the x^{3} coefficient is 1/2 which is the answer D. 