Science:Math Exam Resources/Courses/MATH110/April 2019/Question 07 (a)
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Question 07 (a) 

Using a linear approximation of at , estimate . Simplify your answer. 
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 

Given a differentiable function , the linear approximation of at the point is a function which passes through the point and has the same slope as at that point. Knowing this information, apply it to the function with . 
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 are asked to use the linear approximation of at the point to approximate . This linear approximation, which we denote by , is given by . We already know that , so we need only find . To do so, we apply the power rule, and find that . Substituting this information into our formula for , we have . Then, to estimate the value of , we plug in into our linear approximation. This gives . 