Science:Math Exam Resources/Courses/MATH100/December 2015/Question 06 (b)
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Question 06 (b) 

Estimate using a linear approximation. 
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 

Use the linearization of the square root function at . 
Hint 2 

What is the function to which you apply linear approximation? 
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. Since we know and and 9 is closer to 8, we use the linear approximation of the function at 9. By the formula for linear approximation we know for close to , where in this question and we look for , therefore and . The linearization is:
Therefore, for x close to 9, and hence . 