Science:Math Exam Resources/Courses/MATH200/December 2011/Question 01 (c)
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Question 01 (c) 

Consider the function c) Find the tangent plane approximation to the value of using the tangent plane from part (b). 
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 

The tangent plane you derived in part (b) should provide a good estimate for f(x,y) for values of (x,y) near (2,1). Simply plug in the values of (x,y) into your tangent plane approximation to estimate . 
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. From part (b), we found that the tangent plane to the surface at the point was Since the point is very close to , the tangent plane approximation gives a good estimate for the true value of . Plugging in into the tangent plane equation we get Therefore, 