Science:Math Exam Resources/Courses/MATH104/December 2011/Question 06 (d)
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Question 06 (d) 

In this problem, you will approximate in two ways: one using linear approximation and the other using quadratic approximation. You may find it useful to draw the graph of for near 1 to help you answer some parts of this question. d) Use the quadratic approximation (seconddegree Taylor polynomial) to centred at to approximate . 
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 

What is the formula for a Taylor polynomial of degree 2? What is f(x), what is the a value? 
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. Beginning with definition of the quadratic approximation of a function at a point , we find that the quadratic approximation to at is given by: Thus the quadratic approximation for is: 