Science:Math Exam Resources/Courses/MATH104/December 2013/Question 01 (i)
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Question 01 (i) 

Find an approximation to by using the linear approximation to at . 
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 

Recall that a linear approximation involves finding the equation of the tangent line to at the point . 
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. We use the point slope formula Since we obtain , while implies . Hence
Solving gives
Thus, the approximation we seek is given by . 