Science:Math Exam Resources/Courses/MATH100/December 2011/Question 04 (a)
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Question 04 (a) 

FullSolution Problems. In questions 28, justify your answers and show all your work. If a box is provided, write your final answer there. Simplification of answers is not required unless explicitly stated. Let T_{2}(x) be the second degree Taylor polynomial about a = 8 for Find T_{2}(x) and simplify your answer. 
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 

Recall that the general forumla for a second degree Taylor polynomial is: 
Checking a solution serves two purposes: helping you if, after having used the hint, 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 general forumla for a second degree Taylor polynomial is: To find this for ƒ(x), we need to first find ƒ'(x) and ƒ″(x): And now we can evaluate at a = 8 to get We can now plug these in to the equation for the second Taylor polynomial and obtain: (This is simplified enough for the purpose of Taylor polynomials). 