Science:Math Exam Resources/Courses/MATH100/December 2012/Question 01 (b)
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Question 01 (b) 

ShortAnswer Questions. Questions 14 are shortanswer questions. Put your answers in the boxes provided. Simplify your answers as much as possible, and show your work. Each question is worth 3 marks, but not all questions are of equal difficulty.

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 

There are two key questions we need to think about. Firstly, what would be a good function to use to approximate ? Secondly, what would be a good value to use as a linear approximation? 
Hint 2 

Try using the function and the linear approximation around the point . 
Hint 3 

The linear approximation of ƒ at x = a is given by 
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. Let , so . The linear approximation of at 2 is given by
Thus, 