Science:Math Exam Resources/Courses/MATH104/December 2010/Question 01 (n)
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Question 01 (n) 

Use the linear approximation to ln(x) at x=1 to estimate ln(0.8). 
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 

The graph of the linear approximation taken at is the tangent line to the curve at . 
Hint 2 

The linear approximation to a function at 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. We use the linear approximation of at to estimate . (Approximating at x = 1 is a logical choice, as 1 is close to 0.8, and we know that .) We know , which is equal to 1 when . Substituting this into the linear approximation formula, we get, 