Science:Math Exam Resources/Courses/MATH100/December 2011/Question 01 (m)
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Question 01 (m) 

ShortAnswer Questions. Put your answer in the box provided but show your work also. Each question is worth 3 marks, but not all questions are of equal difficulty. Full marks will be given for correct answers placed in the box, but at most 1 mark will be given for incorrect answers. Unless otherwise stated, it is not necessary to simplify your answers in this question. Use Newton's Method to find the second approximation x_{2} to starting with the inital approximation x_{1}=1. 
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 

How can we turn this into a root finding problem? 
Hint 2 

The formula for Newton's Method is 
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 strength of Newton's method is on root finding. We're asked to approximate which we can write as a root finding problem, With this in mind, let Taking the derivative gives We start with as our first iteration and so if we apply Newton's Method, we get, If we actually compute we get and so is already in good agreement. 